Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsThematic Seminar, Jan 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122704&date=2019-01-15
Density functional theory is an effective tool in solid state physics and quantum chemistry for electronic structure calculation. However, it has difficulties when dealing with strongly correlated systems. In this talk, we examine the regime where the electrons are strictly correlated. This gives rise to a multimarginal optimal transport problem, a direct extension of the optimal transport problem that has applications in economics and operations research as well. In particular we introduce methods from convex optimization to provide a lower bound to the cost of the multimarginal transport problem with a practical running time. We further propose projection schemes based on tensor decomposition to obtain upper bounds to the energy. Numerical experiments demonstrate a gap of order $10^{-3}$ to $10^{-2}$ between the upper and lower bounds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122704&date=2019-01-15Seminar 217, Risk Management: Instrumental variables as bias amplifiers with general outcome and confounding, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122084&date=2019-01-22
Drawing causal inference with observational studies is the central pillar of many disciplines. One sufficient condition for identifying the causal effect is that the treatment-outcome relationship is unconfounded conditional on the observed covariates. It is often believed that the more covariates we condition on, the more plausible this unconfoundedness assumption is. This belief has had a huge impact on practical causal inference, suggesting that we should adjust for all pretreatment covariates. However, when there is unmeasured confounding between the treatment and outcome, estimators adjusting for some pretreatment covariate might have greater bias than estimators that do not adjust for this covariate. This kind of covariate is called a bias amplifier and includes instrumental variables that are independent of the confounder and affect the outcome only through the treatment. Previously, theoretical results for this phenomenon have been established only for linear models. We fill this gap in the literature by providing a general theory, showing that this phenomenon happens under a wide class of models satisfying certain monotonicity assumptions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122084&date=2019-01-223-Manifold Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122912&date=2019-01-22
This semester I plan to cover material about special groups and arithmetic manifolds of simplest type, among other things. We'll overview these topics and results that we plan to cover this semester in the seminar.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122912&date=2019-01-22Differential Geometry Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122775&date=2019-01-22
We show that each fixed point component of an isometric torus action of a 5 torus has the rational cohomology of a rank one symmetric space. We give various applications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122775&date=2019-01-22Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122914&date=2019-01-22
In the past decade, algebraic geometry and representation theory have been used to obtain lower complexity bounds for central problems such as Valiant's algebraic version of P v. NP (permanent v. determinant) and determining the complexity of matrix multiplication. At the same time, complexity theory has raised new, interesting questions in geometry. I will give an overview of these developments and then focus on recent exciting results.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122914&date=2019-01-22Thematic Seminar, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122731&date=2019-01-22
Vasy will discuss, based on joint work with Peter Hintz, the stability of the family of Kerr-de Sitter (KdS) black holes, which are rotating black holes in a spacetime with positive cosmological constant, as solutions of Einstein's vacuum equation: spacetimes evolving from initial data close to those of a KdS metric stay globally close to this KdS spacetime, and are indeed asymptotic to a nearby member of the KdS family.<br />
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Vasy will discuss the general setup and formulate the result, and then in the second half of the talk focus on general analytic aspects of this problem, involving global analysis, together with the choice of a gauge to break the diffeomorphism invariance of Einstein's equation and the role of constraint damping which has also played a key role in numerical general relativity (and thus LIGO and the detection of gravitational waves).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122731&date=2019-01-22Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Jan 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122915&date=2019-01-22
In the past decade, algebraic geometry and representation theory have been used to obtain lower complexity bounds for central problems such as Valiant's algebraic version of P v. NP (permanent v. determinant) and determining the complexity of matrix multiplication. At the same time, complexity theory has raised new, interesting questions in geometry. I will give an overview of these developments and then focus on recent exciting results.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122915&date=2019-01-22Harmonic Analysis Seminar, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123035&date=2019-01-23
The elementary Riesz-Sobolev inequality, which dates to the 1930s, is concerned with the functional $\iint _{\mathbb R^d\times \mathbb R^d} f(x)g(y)h(x+y)\,dx\,dy$, and states that among indicator functions $f,g,h$ of subsets of $\mathbb R^d$ of specified Lebesgue measures, those sets for which the functional attains its maximum value are balls centered at the origin. Burchard's theorem states that under a natural hypothesis on the specified measures, these are the only maximizing configurations, up to a natural action of the group $Sl(d)$ and of translations in $\mathbb R^d$. The Brascamp-Lieb-Luttinger-Rogers inequality generalizes the inequality and involves tuples of linear mappings from $(\mathbb R^d)^m$ to $\mathbb R^d$ that satisfy a certain symmetry hypothesis. A similar characterization of maximizers is known to hold.<br />
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I will discuss some partial results concerning the nature of maximizers of integral functionals of this type when the symmetry hypothesis is dropped, indicating some ingredients in the proofs without full details. Ideas used in the classical theory of Riesz, Sobolev, Brascamp-Lieb-Luttinger, Rogers, and Burchard will also be sketched. The new results are joint work with Dominique Maldague.<br />
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After this exceptional initial meeting, this will be a student-oriented seminar devoted to systematic presentation of relatively recent works of Bourgain-Demeter and of Guth.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123035&date=2019-01-23Topology Seminar (Introductory Talk), Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122909&date=2019-01-23
This will be an introductory talk to Dirichlet domain and volume computations in \(H^3\). We'll give a definition of a Dirichlet domain and discuss its tiling properties. Then we explore volume computation in a hyperbolic case. We review few special cases: orthoscheme, ideal tetrahedron and a tetrahedron with one ideal vertex. Then we generalize these computations for volume of any polyhedron in Hyperbolic Space. No background in Hyperbolic Geometry is required.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122909&date=2019-01-23Number Theory Seminar, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122942&date=2019-01-23
This semester the seminar focuses on Hodge cycles on abelian varieties. I will give an introductory talk and then we discuss the organization of the seminar.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122942&date=2019-01-23Thematic Seminar, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122835&date=2019-01-23
Families of algebraic manifolds give interesting examples of discrete subgroups of Lie groups, via their monodromy. They also lead to differential equations, such as the hypergeometric ones, whose solutions have an arithmetic significance. After providing the necessary background I will explain a connection to dynamical invariants called Lyapunov exponents, which reveals special geometric features ofthe discrete groups and the corresponding differential equations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122835&date=2019-01-23Topology Seminar (Main Talk), Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122910&date=2019-01-23
In this talk we address some problems concerning an approximate Dirichlet domain. We show that under some assumptions the approximate Dirichlet domain can work equally well as an exact Dirichlet domain. In particular, we consider a problem of tiling a hyperbolic ball with copies of the Dirichlet domain. This problem arises in the construction of the length spectrum algorithm which is for example implemented by the computer program SnapPea. Our result explains the empirical fact that the program works surprisingly well despite it does not use exact data. Also we demonstrate a rigorous verification if two words of a fundamental group of a hyperbolic 3-manifold are the same or not.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122910&date=2019-01-23Paris/Berkeley/Bonn/Zürich Analysis Seminar, Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122605&date=2019-01-24
In this talk, we study the long time behaviour of some stochastic partial differential equations (SPDEs). After introducing the notions of ergodicity, unique ergodicity and convergence to equilibrium, we will discuss how these have been proven for a very large class of parabolic SPDEs.<br />
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We will then shift our attention to dispersive SPDEs, where the general strategy for the parabolic case fails. We will describe this failure for wave equation on the 1-dimensional torus and present a result that settles unique ergodicity even in this case.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122605&date=2019-01-24CANCELED: Thematic Seminar, Jan 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122836&date=2019-01-24
Let $M_g$ be the moduli space of smooth curves of genus $g$. The tautological ring is a subring of the cohomology of $M_g$ that was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of the tautological ring. After reviewing these conjectures, I will discuss some of the evidence in recent years favoring one conjecture over the other.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122836&date=2019-01-24Student 3-Manifold Seminar, Jan 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123095&date=2019-01-25
This is an organizational meeting for this learning seminar. We will additionally discuss the existence and uniqueness of prime decompositions for connected, oriented, compact 3-manifolds, due to Kneser and Milnor.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123095&date=2019-01-25Thematic Seminar, Jan 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122837&date=2019-01-25
The classical $q$-hypergeometric orthogonal polynomials are assembled into a hierarchy called the $q$-Askey scheme. It is now a classical subject to study the combinatorics of their coefficients and their moments. The polynomials admit a generalization leading to remarkable orthogonal polynomials in several variables. The most general family is the Macdonald-Koornwinder polynomials and Macdonald polynomials associated to any classical root system can be expressed as limits or special cases of Macdonald-Koornwinder polynomials. Understanding the combinatorics of these polynomials is an important open problem. In this talk we will show some recent progress related to special cases of these polynomials.<br />
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We will highlight combinatorial formulas for<br />
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1. Certain Macdonald-Koornwinder polynomials using exclusion processes with open boundaries and tableaux combinatorics (arXiv:1510.05023)<br />
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2. Macdonald polynomials of type A using exclusion processes and multiline queues (arXiv:1811.01024)<br />
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3. Multivariate $q$-Little Jacobi polynomials thanks to Lecture Hall Tableaux (arXiv:1804.02489)<br />
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This talk will be about enumerative, algebraic and asymptotics combinatorics. No prior knowledge is required. Open problems will be presented.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122837&date=2019-01-25Combinatorics Seminar, Jan 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123034&date=2019-01-28
Twenty-five years ago, Stanley introduced local h-polynomials for subdivisions of simplices, proved that the coefficients are non-negative integers, and posed the problem of characterizing triangulations for which this invariant vanishes. The work I will present is motivated by potential applications in other areas of mathematics (local h-polynomials now appear prominently in both algebraic and arithmetic geometry, through relations to intersection cohomology) yet the statements and proofs are purely combinatorial. The main results resolve Stanley's question in dimension 2 and 3, and give some promising first steps in higher dimensions. Joint with Elijah Gunther, Andre Moura, Jason Schuchardt, and Alan Stapledon.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123034&date=2019-01-28Probabilistic Operator Algebra Seminar, Jan 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122179&date=2019-01-28
We present an alternative approach to the theory of free Gibbs states with convex potentials. Instead of solving SDE's, we combine PDE techniques with a notion of asymptotic approximability by trace polynomials for a sequence of functions on $M_N(\mathbb C)_{sa}^m$ to prove the following. Suppose $\mu _N$ is a probability measure on $M_N(\mathbb C)_{sa}^m$ given by uniformly convex and semi-concave potentials $V_N$, and suppose that the sequence $DV_N$ is asymptotically approximable by trace polynomials. Then the moments of $\mu _N$ converge to a noncommutative law λ. Moreover, the free entropies $\chi (\lambda )$, $\underline {\chi }(\lambda )$, and $\chi ^*(\lambda )$ agree and equal the limit of the normalized classical entropies of $\mu _N$. We also sketch further applications to conditional expectations, relative entropy, and free transport for these free Gibbs states.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122179&date=2019-01-28String-Math Seminar, Jan 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123096&date=2019-01-28
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. We describe a deformation of this correspondence for \(SL(N)\). We introduce a difference equation version of opers called q-opers and prove a q-Langlands correspondence between nondegenerate solutions of the Bethe ansatz equations for the \(XXZ\) model and nondegenerate twisted q-opers with regular singularities on the projective line. We show that the quantum/classical duality between the \(XXZ\) spin chain and the trigonometric Ruijsenaars-Schneider model may be viewed as a special case of the q-Langlands correspondence. We also describe an application of q-opers to the equivariant quantum K-theory of the cotangent bundles to partial flag varieties.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123096&date=2019-01-28Arithmetic Geometry and Number Theory RTG Seminar, Jan 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123094&date=2019-01-28
Using the Eisenbud–Khimshiashvili–Levine local degree, which is the A1-local degree of Morel in A1-homotopy theory, we define a degree of a finite map between smooth schemes over k. When the target is appropriately connected, this degree is a bilinear form over k. We discuss some applications to enumerative geometry over non-algebraically closed fields. This is joint work with Jesse Kass and Jake Solomon, and will also contain joint work with Padmavathi Srinivasan.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123094&date=2019-01-28Differential Geometry Seminar, Jan 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122886&date=2019-01-28
A longstanding problem in mirror symmetry has been to understand the relationship between the existence of solutions to certain geometric nonlinear PDES (the special Lagrangian equation, and the deformed Hermitian-Yang-Mills equation) and algebraic notions of stability, mainly in the sense of Bridgeland. I will discuss progress in this direction through ideas originating in infinite dimensional GIT. This is joint work with S.-T. Yau.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122886&date=2019-01-28Support points – a new way to reduce big and high-dimensional data, Jan 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123085&date=2019-01-28
This talk presents a new method for reducing big and high-dimensional data into a smaller dataset, called support points (SPs). In an era where data is plentiful but downstream analysis is oftentimes expensive, SPs can be used to tackle many big data challenges in statistics, engineering and machine learning. SPs have two key advantages over existing methods. First, SPs provide optimal and model-free reduction of big data for a broad range of downstream analyses. Second, SPs can be efficiently computed via parallelized difference-of-convex optimization; this allows us to reduce millions of data points to a representative dataset in mere seconds. SPs also enjoy appealing theoretical guarantees, including distributional convergence and improved reduction over random sampling and clustering-based methods. The effectiveness of SPs is then demonstrated in two real-world applications, the first for reducing long Markov Chain Monte Carlo (MCMC) chains for rocket engine design, and the second for data reduction in computationally intensive predictive modeling.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123085&date=2019-01-28Seminar 217, Risk Management: The coordination of centralised and distributed generation, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122085&date=2019-01-29
We analyse the interaction between centralised carbon-emissive technologies and distributed non-emissive technologies. A representative consumer can satisfy her electricity demand by investing in solar panels and by buying power from a centralised firm. We consider the point of view of the consumer, the firm and a social planner, formulating suitable McKean-Vlasov control problems with stochastic coefficients. First, we provide explicit formulas for the production strategies which minimise the costs. Then, we look for an equilibrium price. Joint work with René Aid and Huyen Pham.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122085&date=2019-01-29Student Harmonic Analysis and PDE Seminar (HADES), Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122840&date=2019-01-29
The Remez inequality for polynomials states that the maximum of the polynomial over an interval is controlled by its maximum over a subset of the interval of positive measure. The coefficient in the inequality depends on the degree of the polynomial and the result holds in higher dimensions.<br />
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We give a version of the Remez inequality for solutions of second order linear elliptic PDEs and their gradients. In this context, the degree of a polynomial is replaced by the Almgren frequency of the solution. We discuss other results on quantitative unique continuation for solutions of elliptic PDEs and their gradients and give some applications for the estimates of eigenfunctions for the Laplace-Beltrami operator. The talk is based on a joint work with A. Logunov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122840&date=2019-01-293-Manifold Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123214&date=2019-01-29
<b>Note the new time and location</b> We will continue to discuss hyperbolic orbifolds of simplest type, describing a criterion for compactness via the Mahler compactness theorem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123214&date=2019-01-29Representation Theory and Mathematical Physics Seminar, Jan 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123212&date=2019-01-29
The talk will start with a reminder of what is a Hamiltonian integrable system and what degenerate integrability, also know as superintegrability, means. Then examples of such systems on symplectic leaves of Poisson variety \(K\backslash T^*G/K\) will be constructed for a Lie group \(G\) and a Lie subgroup \(K\subset G\). If \(G\) is a simple Lie group and \(K\) is the subgroup of fixed points of the Chevalley automorphism of \(G\), Hamiltonians of such integrable systems will be described explicitly.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123212&date=2019-01-29Harmonic Analysis Seminar, Jan 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123318&date=2019-01-30
The Riesz-Sobolev inequality states that for indicator functions $f,g,h$ of subsets of $ℝ^d$ of specified measure, the functional $\iint_{ℝ^d\times ℝ^d} f(x)g(y)h(x+y)dxdy$ is maximized when the subsets are balls centered at the origin. Burchard '96 showed that under suitable hypotheses, the functional is maximized precisely when the subsets are balls centered at the origin and their orbit under its symmetries (translation and the diagonal action of the special linear group).<br />
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In this talk, I will discuss a similar characterization of maximizers for a generalization of the Riesz-Sobolev inequality known as the Rogers-Bracsamp-Lieb-Luttinger inequality. A byproduct of the method of proof is a sharpened version of the Rogers-Brascamp-Lieb-Luttinger inequality, controlling the underlying functional by its value when the sets are balls centered at the origin minus a quadratic term involving the distance of the given sets from maximizers.<br />
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Results are joint work with Michael Christ.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123318&date=2019-01-30CANCELED: Topology Seminar (Introductory Talk), Jan 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122838&date=2019-01-30
Fix a suitable (non-elementary) map $f$ from a closed surface $S$ into a closed hyperbolic 3-manifold $M$, and consider the moduli space of harmonic maps homotopic to $f$ and with respect to varying metrics on $S$ and $M$ (the metrics on $M$ are assumed to be negatively curved). We show that the set of such metrics for which the corresponding harmonic map is in Whitney's general position is an open, dense, and connected subset of this moduli space. One application of this result is the proof of the special case of the Simple Loop conjecture when $M$ is hyperbolic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122838&date=2019-01-30Number Theory Seminar, Jan 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123355&date=2019-01-30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123355&date=2019-01-30CANCELED: Topology Seminar (Main Talk), Jan 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122839&date=2019-01-30
Fix a suitable (non-elementary) map $f$ from a closed surface $S$ into a closed hyperbolic 3-manifold $M$, and consider the moduli space of harmonic maps homotopic to $f$ and with respect to varying metrics on $S$ and $M$ (the metrics on $M$ are assumed to be negatively curved). We show that the set of such metrics for which the corresponding harmonic map is in Whitney's general position is an open, dense, and connected subset of this moduli space. One application of this result is the proof of the special case of the Simple Loop conjecture when $M$ is hyperbolic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122839&date=2019-01-30The Stratified Micro-randomized Trial Design: Sample Size Considerations for Testing Nested Causal Effects of Time-varying Treatment, Jan 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123086&date=2019-01-30
Technological advancements in the field of mobile devices and wearable sensors have helped overcome obstacles in the delivery of care, making it possible to deliver behavioral treatments anytime and anywhere. Delivery of these treatments is increasingly triggered by detections/predictions of vulnerability and receptivity, which may have been impacted by prior treatments. Furthermore the treatments are often designed to have an impact on users over a span of time during which subsequent treatments may be provided. In this talk, I will discuss the design of a mobile health smoking cessation intervention study with the goal of assessing whether reminders, delivered at times of stress, result in a reduction/prevention of stress in the near-term, and whether this effect changes with time in study. Multiple statistical challenges arose in this effort, leading to the development of the ``stratified micro-randomized trial'' design. In these designs, each individual is randomized to treatment repeatedly at times determined by predictions of risk. These "risk" times may be impacted by prior treatment. I will describe the statistical challenges and detail how they can be met.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123086&date=2019-01-30DiPerna Lecture, Jan 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123140&date=2019-01-31
We will consider the question on whether we can determine the structure of space time by making measurements near the worldline of an observer. We will consider both active and passive measurements. For the case of passive measurements one measures the fronts of light sources near the observer. For the case of active measurements we couple Einstein equations with matter or electromagnetic fields and formulate the question of determining the structure of space time as the problem of recovering the metric from observations of waves near the observer, The method applies to several other inverse problems for nonlinear equations, for example, nonlinear elastic equations. No previous knowledge of Einstein's equations or Lorentzian geometry will be assumed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123140&date=2019-01-31Dissecting Gene Regulation with Machine Learning: Discoveries and Challenges, Jan 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123216&date=2019-01-31
Machine learning is a popular statistical approach in many fields, including genomics. We and others have used a variety of supervised machine-learning techniques to predict genes, regulatory elements, 3D interactions between regulatory elements and their target genes, and the effects of mutations on regulatory element function. I will highlight a few of these studies, emphasizing the strengths and weaknesses of different predictive models and the biological insights gained via variable importance analysis. Then I will talk about some of our recent work exploring the limitations of popular machine-learning methods in genomics, where the biology underlying the data used to train the models frequently violates one or both parts of the independent and identically distributed (IID) assumption. The talk will conclude with some thoughts on modeling non-IID data and interpreting over-fit models, with the aim of improving the application of supervised learning to biological data and emphasizing the mechanistic insights gained from modeling over performance statistics per se.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123216&date=2019-01-31Student Probability/PDE Seminar, Feb 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123242&date=2019-02-01
Rezakhanlou has shown that the hydrodynamic behaviour of ASEP and other attractive asymmetric particle processes on $R^d$ is governed by a class of conservation laws. That is, macroscopic particle density profiles are given by entropy solutions of these conservation laws. In this talk, we will discuss Bahadoran’s recent extension of these results to bounded domains with particle reservoirs at the boundaries, and, if time permits, implications for hydrostatics and phase transitions. No prior knowledge of particle systems or conversation laws is necessary.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123242&date=2019-02-01Student Arithmetic Geometry Seminar, Feb 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123493&date=2019-02-01
In 2008, Bjorn Poonen announced the construction of a variety without rational points but no étale-Brauer obstruction to the existence of rational points. We attempt to create a new obstruction that explains Poonen s example by applying the étale-Brauer obstruction to a Zariski open cover of a variety. On the one hand, we prove a general result stating that this new obstruction explains every variety without rational points, over quadratic imaginary and totally real number fields. On the other hand, this method is not effective, as the set of adelic points of a non-proper variety is non-compact. Nonetheless, we show how this new obstruction can be applied in Poonen s example. In doing so, we analyze the example from an algebro-topological perspective via the étale homotopy obstruction of Harpaz-Schlank and prove some results of independent interest in this direction.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123493&date=2019-02-01Combinatorics Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122944&date=2019-02-04
We discuss recent developments in combinatorial algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family, we obtain an algebraic variety with interesting properties. Combinatorialists will especially enjoy the role played by Lyndon words and free Lie algebras.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122944&date=2019-02-04String-Math Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123316&date=2019-02-04
I will present the rank \(N\) magnificent four theory, which is the supersymmetric localization of \(U(N)\) super-Yang-Mills theory with matter on a Calabi-Yau fourfold, and conjecture an explicit formula for the partition function \(Z\): it has a free-field representation, and surprisingly it depends on Coulomb and mass parameters in a simple way. Based on joint work with N.Nekrasov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123316&date=2019-02-04Probabilistic Operator Algebra Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123317&date=2019-02-04
In non-commutative probability the notion of stochastic independence is not unique. Therefore an extension of free probability which produces a larger variety of limit laws is certainly of interest. In this seminar we will review the notion of conditional freeness, introduced by Bozejko and Speicher. We will survey some of the combinatorial and analytic tools that are used in this setting and obtain the corresponding limit theorems. For example, a central limit theorem will be deduced, with instances of the limiting distributions including the arcsine, semicircle and Bernoulli distributions and certain deformations of these.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123317&date=2019-02-04Northern California Symplectic Geometry Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123490&date=2019-02-04
In this talk, I will discuss our understanding of contact submanifolds in higher dimensions. First, I will introduce the problems we are interested in and the current techniques we have to address them. In the main focus of the talk, I will present the construction of contactomorphic (and smoothly isotopic) contact submanifolds which are actually not contact isotopic. This resolves one of the main questions we had in higher dimensions. Finally, I will be introducing related works in progress and lines of future development. This talk is partially based on my work with J. Etnyre.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123490&date=2019-02-04Differential Geometry Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122887&date=2019-02-04
Cone spherical metrics are conformal metrics with constant curvature one with finitely many conical singularities on compact Riemann surfaces. The existence problem of such metrics has been open over twenty years. I will introduce the respectful audience some progress on this problem joint with Qing Chen, Xuemiao Chen, Yiran Cheng, Bo Li, Lingguang Li, Santai Qu, Jijian Song, Yingyi Wu and Xuwen Zhu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122887&date=2019-02-04Statistical inference for infectious disease modeling, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123087&date=2019-02-04
We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. We show that when the underlying graph is a tree with certain regularity properties and the structure of the graph is known, confidence sets may be constructed with cardinality independent of the size of the infection set. In the scenario, the goal is to infer the network structure of the underlying graph based on knowledge of the infected individuals. We develop a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the graphs involved in the hypothesis test.<br />
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This is joint work with Justin Khim (UPenn).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123087&date=2019-02-04Northern California Symplectic Geometry Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123491&date=2019-02-04
The aim of this talk is to present a first attempt towards homotopy classification of holomorphic contact structures on Stein manifolds. We introduce the notion of a formal complex contact structure and show that any such structure on an odd dimensional Stein manifold $X$ is homotopic (through formal contact structures) to a genuine holomorphic contact structure on a Stein domain in X which is diffeotopic to $X$. The parametric h-principle also holds in this setting. On Stein threefolds we have a complete homotopy classification of formal complex contact structures. It is currently not understood whether these holomorphic contact structures could be realized on the whole Stein manifold $X$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123491&date=2019-02-04Seminar 217, Risk Management: Endogenous risk, indirect contagion and systemic risk, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122086&date=2019-02-05
Deleveraging by financial institutions in response to losses may lead to contagion of losses across institutions with common asset holdings. Unlike direct contagion via counterparty exposures, this channel of contagion -which we call indirect contagion- is mediated through market prices and does not require bilateral exposures or relations. We show nevertheless that indirect contagion in the financial system may be modeled as a contagion process on an auxiliary network defined in terms of 'liquidity weighted portfolio overlaps' and we study various properties of this network using data from EU banks. Exposure to price-mediated contagion leads to the concept of indirect exposure to an asset class, as a consequence of which the risk exposure of a portfolio strongly depends on the asset holdings of large institutions in the network. We propose a systemic stress testing methodology for evaluating this risk exposure and construct a simple indicator of bank-level exposure to indirect contagion – the Indirect Contagion Index – based on the analysis of liquidity-weighted overlaps across bank portfolios. This indicator is shown to be strongly correlated with bank losses due to deleveraging and may be used to quantify the contribution of a financial institution to price-mediated contagion. <br />
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Joint work with Eric Schaanning (European Systemic Risk Board).<br />
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References:<br />
[1] Rama Cont, Eric F Schaanning (2016) Fire Sales, Indirect Contagion and Systemic Stress Testing. https://ssrn.com/abstract=2541114<br />
[2] Rama Cont, Eric F Schaanning (2017) Monitoring Indirect Contagion. https://ssrn.com/abstract=3195174http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122086&date=2019-02-053-Manifold Seminar, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123594&date=2019-02-05
A cube complex is a cell complex in which each n-cell is a n-dimensional cube. We'll define "special" cube complexes and explain their relationship to right-angled Artin groups. We'll also discuss some results about separability in their fundamental groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123594&date=2019-02-053-Manifold Seminar, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123595&date=2019-02-05
A cube complex is a cell complex in which each n-cell is a n-dimensional cube. We'll define "special" cube complexes and explain their relationship to right-angled Artin groups. We'll also discuss some results about separability in their fundamental groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123595&date=2019-02-05Representation Theory and Mathematical Physics Seminar, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123315&date=2019-02-05
We define the action of infinitely generated Temperley-Lieb algebra on the category of representations of the supergroup \(P(n)\). The supergroup in question is an interesting super analogue of the orthogonal and symplectic groups. As an application of this construction we get algorithm computing characters of irreducible representation of \(P(n)\) and some other esults. As n tends to infinity, we obtain a new universal tensor category equipped with Temperley-Lieb algebra action. In this way we obtain representation of TL in the Fock space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123315&date=2019-02-05Harmonic Analysis Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123518&date=2019-02-06
Introduction to the work of L. Guth on application of the method of polynomial partitioning to Fourier restriction inequalities. This will be the first of a series of seminar meetings devoted to the 2016 article of Guth on this topic. Key concepts will be introduced. The method will be illustrated through an application to a simpler problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123518&date=2019-02-06Topology Seminar (Introductory Talk), Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123519&date=2019-02-06
We'll review the definition of Ozsvath-Szabo's Heegaard Floer homology, and then define the involutive version constructed by Hendricks and Manolescu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123519&date=2019-02-06A phase transition in a spatial permutation model on infinite trees, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123432&date=2019-02-06
Abstract: Spatial random permutation models are of physical interest due to connections to representations of certain gases such as helium as well as of the quantum Heisenberg ferromagnet. Physical phase transitions in these contexts correspond to the appearance of macro or infinite cycles in the permutation model. We study a spatial random permutation model on infinite trees with a time parameter T, a special case of which is the random stirring or random interchange process. The model on trees was first analysed by Björnberg and Ueltschi, who established the existence of infinite cycles for T slightly above a putatively identified critical value but left open behaviour at arbitrarily high values of T. We show the existence of infinite cycles for all T greater than a constant, thus classifying behaviour for all values of T and establishing the existence of a sharp phase transition. Our argument analyses a variant of simple random walk on the tree which is closely related.<br />
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Work with Alan Hammondhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123432&date=2019-02-06Number Theory Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123596&date=2019-02-06
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123596&date=2019-02-06Thematic Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123593&date=2019-02-06
Let Mg be the moduli space of smooth curves of genus g. The tautological ring is a subring of the cohomology of Mg that was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of the tautological ring. After reviewing these conjectures, I will discuss some of the evidence in recent years favoring one conjecture over the other.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123593&date=2019-02-06Center for Computational Biology Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120946&date=2019-02-06
Genomics, genetic rescue, and the future of conservation<br />
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Abstract: New technologies, including complete genome sequencing and genome engineering, promise to revolutionize conservation and slow the pace of the ongoing extinction crisis. However, the value of these technologies to conservation remains unclear. Using mountain lions from across their range and wolves from Isle Royale as examples, I will explore the value of complete genome reconstruction and analysis to conservation and management, focusing on what complete genomes can reveal that traditional genetic approaches cannot. I will also discuss the potential of genomics to inform genetic rescue interventions, and highlight some of the technical, ethical, and environmental hurdles that these particularly controversial technologies still face.<br />
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Bio: Beth Shapiro is an evolutionary biologist who specializes in the genetics of ice age animals and plants. As Professor of Ecology and Evolutionary Biology at UC Santa Cruz and HHMI Investigator, Beth uses DNA recovered from bones and other remains to study how species evolved through time and how human activities have affected and continue to affect this dynamic process. Her work focuses on organisms ranging from influenza to mammoths, asking questions about domestication, admixture, speciation, and pathogen evolution. Her current work develops techniques to recover increasingly trace amounts of DNA such as from environmental and forensic samples.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120946&date=2019-02-06Topology Seminar (Main Talk), Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123149&date=2019-02-06
We explain a generalization of the techniques that Hom introduced to construct an infinite-rank summand of the topologically slice knot concordance group. We generalize Hom's epsilon-invariant to the involutive Heegaard Floer homology constructed by Hendricks-Manolescu. As an application, we see that there is an infinite-rank summand of the homology cobordism group. This is joint work with Irving Dai, Jen Hom, and Linh Truong.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123149&date=2019-02-06Applied Math Seminar, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122772&date=2019-02-07
In this talk we discuss how to compute derivatives of long-time-averaged objectives with respect to multiple system parameters in chaotic systems, via the recently developed non-intrusive least-squares adjoint shadowing (NILSAS) algorithm.<br />
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First we review how to compute such derivatives via comparing the base trajectory and a shadowing trajectory, which is a new trajectory with perturbed parameter and perturbed initial condition, yet always lies close to the base trajectory. Then we review how to compute such shadowing trajectory via a `non-intrusive' minimization problem on the unstable subspace. Then we show our recent work on defining and proving the unique existence of adjoint shadowing directions. Then we develop the NILSAS algorithm, whose cost is independent of number of parameters, and its implementation requires only minor modifications to existing adjoint solvers. Finally, we show an application, by Chaitanya Talnikar, of NILSAS on a weakly turbulent flow over a three-dimensional cylinder at Re=1100, where the cost of NILSAS is similar to simulating the flow problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122772&date=2019-02-07Special Seminar, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123676&date=2019-02-07
Tschinkel will discuss effectivity issues in several problems in arithmetic geometry, the study of solutions of systems of polynomial equations with integral coefficients.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123676&date=2019-02-07Inverse RNA folding and Computational Riboswitch Detection, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123217&date=2019-02-07
The inverse RNA folding problem for designing sequences that fold into a given RNA secondary structure was introduced in the early 1990's in Vienna. Using a coarse-grain tree graph representation of the RNA secondary structure, we extended the inverse RNA folding problem to include constraints such as thermodynamic stability and mutational robustness, developing a program called RNAexinv. In the next step, we formulated a fragment-based design approach of RNA sequences that can be useful to practitioners in a variety of biological applications. In this shape-based design approach, specific RNA structural motifs with known biological functions are strictly enforced while others can possess more flexibility in their structure in favor of preserving physical attributes and additional constraints. Our program is called RNAfbinv (recently extended to incaRNAfbinv by incorporating a weighted sampling approach borrowed from incaRNAtion).<br />
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Detection of riboswitches in genomic sequences using structure based methods, including the use of incaRNAfbinv, will also be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123217&date=2019-02-07Mathematics Department Colloquium, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123590&date=2019-02-07
A conjecture of Kontsevich says that the Fukaya category of a symplectic manifold having an additional volume form, should have a stability condition where the stable objects are represented by possibly singular "special Lagrangians". This statement has a nice expression, in the case where we look at the Fukaya-Seidel category of a Riemann surface with coefficients in a fiber category. The special Lagrangians are identified with the spectral networks of Gaiotto-Moore-Neitzke. In joint work with Haiden, Katzarkov and Pandit, in progress, we treat a first rather simple case but one that leads already to some interesting pictures.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123590&date=2019-02-07GRASP seminar, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123723&date=2019-02-08
Given a real polynomial $p$ in $n$-variables, we define a family of distributions over $\{\lambda \in \mathbb C | \text {Re}\lambda >0\}$, generalizing the Γ-function. We claim that it is possible to analytically continue this family, exactly the same way as is traditionally done for the Γ-function, using the existence of the so-called Bernstein-Sato polynomial, $b_p$, of $p$.<br />
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We compute some of examples of these polynomials, then show that their existence is equivalent to a purely module-theoretical question. This takes us into the theory of holonomic $\mathcal D$-modules on $\mathbb A^n$, which we shall use as a diving board into the theory of $\mathcal D$-modules and to solve the original analytic question.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123723&date=2019-02-08A planet-scale playground for data scientists - Google Maps, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123494&date=2019-02-08
Are there good soba noodle places nearby? How do I get to JFK by train? When does this park close? Show me Stonehenge! Helping people explore and get things done in the real world is the task our team has taken on, and it is a rather challenging one. In this talk I will describe the technical complexity of creating models that reflect the real world for tools such as Google Maps, Search and Google Earth.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123494&date=2019-02-08Logic Colloquium, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123314&date=2019-02-08
I will present a few basic applications of model theory in theoretical computer science, e.g. in verification, databases, and algorithms. I will also briefly discuss some links between notions from graph theory and stability theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123314&date=2019-02-08Student 3-Manifold Seminar, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123675&date=2019-02-08
Simplified, the loop theorem states that if the induced map $\pi _1(\partial M)\to \pi _1(M)$ for a $3$-manifold $M$ is not injective, then there is a nullhomotopy of an essential loop in $\partial M$ that can be represented by an embedded disk. We will go through the proof of Stalling's formulation of the loop theorem using Papakyriakopoulos's tower construction and discuss some applications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123675&date=2019-02-08Student Arithmetic Geometry Seminar, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123722&date=2019-02-08
Last week, I explained the (etale) Brauer-Manin obstruction and Poonen's counterexample. I also stated my result that the Brauer-Manin obstruction on Zariski open covers is enough to (theoretically) determine the existence of rational points. This week, I will say more about how to prove this result. I will also explain the idea behind the etale homotopy obstruction to the local-global principle and how it sheds new light on the more classical obstructions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123722&date=2019-02-08Combinatorics Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122943&date=2019-02-11
In an n-team tournament, each pair of teams plays a win-lose match. Landau's Theorem (1953) states that a sequence (x1,x2,...,xn), written in non-decreasing order, is the score sequence of some n-team tournament if and only if it is majorized by (0,1,...,n-1), meaning that all partial sums x1+...+xk are at least k(k-1)/2, with equality for k=n. Moon's Theorem (1963) extends this to random tournaments, in which case x is the mean score sequence. We give two short, probabilistic proofs of Moon's Theorem, one of which is fully constructive. We also show that the set of mean score sequences is the closure of those arising from the Bradley-Terry model (a model for sports results), where for a sequence of abilities (a1,a2,...,an), the probability that team i beats j is L(ai-aj), where $L(x)=e^x/(1+e^x)$ is the logistic function. This talk offers a glimpse into a longstanding mystery: the lack of a canonical construction for a joint distribution in the representation theorem (Strassen 1965) for convex order. This is joint work with David Aldous.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122943&date=2019-02-11Probabilistic Operator Algebra Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122178&date=2019-02-11
It is known that the property of being free (or asymptotically free) for Haar unitaries remains to some extent, when the unitaries are tensored with other unitaries. In the recent years, we investigated the question of, to which extent this property holds. For example, does it hold when tensored by non-unitary operators ? When does asymptotic freeness hold strongly (in norm) ? In traffics ? etc. We have complete answers to some questions, and partial answers to others. I will review what is known at this point. This talk is based on various papers in collaboration with people including Charles Bordenave (CNRS), Camille Male (CNRS), and Pierre Ives Gaudreau Lamarre (Princeton).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122178&date=2019-02-11Daniel Lacker - Beyond Mean Field Limits: Local Dynamics For Large Sparse Networks Of Interacting Diffusions, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123363&date=2019-02-11
Abstract: We study large systems of stochastic processes (particles) in which each particle is associated with a vertex in a graph and interacts only with its neighbors. When the graph is complete and the numbers of particles grows to infinity, the system is well-described by a McKean-Vlasov equation, which describes the behavior of one typical particle. For general (sparse) graphs, the system is no longer exchangeable, and the mean field approximation is not valid. Nevertheless, if the underlying graph is locally tree-like, we show that a single particle and its nearest neighbors are characterized by a peculiar but autonomous set of "local dynamics." This work is motivated in part by recent mean field models of inter-bank lending, which capture several dynamic features of systemic risk but thus far lack realistic network structure. Joint work with Kavita Ramanan and Ruoyu Wu.<br />
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Bio: Daniel Lacker is an assistant professor in Industrial Engineering and Operations Research (IEOR) at Columbia University. From 2015-2017 he was an NSF postdoctoral fellow in Applied Mathematics at Brown University, and before that he completed his Ph.D. in 2015 at Princeton University in the department of Operations Research and Financial Engineering (ORFE). So far his research has focused largely on the theory and applications of mean field games, where the areas of interacting particle systems, stochastic control, and game theory intersect. More broadly, he is interested in many topics in probability and mathematical finance.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123363&date=2019-02-11String-Math Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123492&date=2019-02-11
A classical result of Turaev identifies the skein algebra of the annulus with the algebra of symmetric functions in infinitely many variables. Queffelec and Roze categorified this using annular webs and foams. I will recall their construction and compute explicit symmetric functions and their categorical analogues for some links. As an application, I will describe spectral sequences computing categorical invariants of generalized Hopf links. The talk is based on a joint work with Paul Wedrich.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123492&date=2019-02-11Arithmetic Geometry and Number Theory RTG Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123517&date=2019-02-11
The topology of an algebraic variety is a central subject in algebraic geometry. Instead of a variety, we consider the topology of a pair (X,D) which is a variety X with a divisor D, but in the coarsest level. More precisely, we study the dual complex defined as the combinatorial datum characterizing how the components of D intersect with each other. We will discuss how to use the minimal model program (MMP) to investigate it. We will also discuss some applications, including in the construction of non-archimedean SYZ fibrations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123517&date=2019-02-11Chiwei Yan - Transportation Optimization: Data-enabled Advances in a Sharing Economy, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122323&date=2019-02-11
Abstract: The transportation and logistics industries are undergoing a round of revolutionary innovation. This innovation is fueled by two key drivers: (1) the growing availability of data, and (2) new operational paradigms in a sharing economy. This talk focuses on showcasing how new models, enabled by the prevalence of data, can lead to significant value in operational decision-making.<br />
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We begin by presenting our research that shows how trip data in bike-sharing systems can be mined to infer rider substitution behaviors when there are bike or dock shortages. Based on a non-parametric ranking-based choice model, we propose efficient enumeration procedures and first-order methods to solve the large-scale estimation problem by exploiting problem structure. We prove consistency results of our method. We then demonstrate, with Boston Hubway data, that ridership can be significantly improved through effective inventory allocation operations with better demand modeling.<br />
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Next, we describe a recent work in which we propose a new car-pooling mechanism in ride-hailing, called dynamic waiting which varies rider waiting before dispatch. The goal is to limit price volatility in ride-hailing services by reducing the role of surge pricing. We describe a steady-state model depicting the long-run average performance of a ride-hailing service, and characterize the system equilibrium. Calibrating the model using Uber data, we reveal insights on welfare-maximizing pricing and waiting strategies. We show that, with dynamic waiting, price can be lowered, its variability is mitigated and total welfare is increased. <br />
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Bio: Chiwei Yan received his PhD from the Operations Research Center at MIT in 2017. His current research interest is in transportation and logistics, with a focus on data-driven optimization and emerging problems in a sharing economy. He is a recipient of the Best Dissertation Award Honorable Mention and the Outstanding Paper Award in Air Transportation from INFORMS Transportation Science and Logistics Society, the Best Dissertation Award from INFORMS Aviation Application Section, the AGIFORS Anna Valicek Award, and the UPS Doctoral Fellowship, among others. His research involves collaborations with both the private and public sectors, including the Federal Aviation Administration, Sabre Airline Solutions, Boston Hubway Bikes and Uber. Before coming to MIT, he obtained the Bachelor of Science in Industrial Engineering from Tsinghua University.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122323&date=2019-02-11Analysis and PDE Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123592&date=2019-02-11
A control system is a dynamical system on which one can act thanks to what is called the control. For example, in a car, one can turn the steering wheel, press the accelerator pedal etc. These are the control(s). One of the main problems in control theory is the controllability problem. One starts from a given situation and there is a given target. The controllability problem is to see if, by using some suitable controls depending on time, one can move from the given situation to the desired target. We study this problem with a special emphasis on the case where the nonlinearities play a crucial role. We first recall some classical results on this problem for finite dimensional control systems. We explain why the main tool used for this problem in finite dimension, namely the iterated Lie brackets, is difficult to use for many important control systems modeled by partial differential equations. We present methods to avoid the use of these iterated Lie brackets. We give applications of these methods to various physical control systems (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg-de Vries equations).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123592&date=2019-02-11Seminar 217, Risk Management: Computation of Optimal Conditional Expected Drawdown Portfolios, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122087&date=2019-02-12
We introduce two approaches to computing and minimizing the risk measure Conditional Expected Drawdown (CED) of Goldberg and Mahmoud (2016). One approach is based on a continuous-time formulation yielding a partial differential equation (PDE) solution to computing and minimizing CED while another is a sampling based approach utilizing a linear program (LP) for minimizing CED.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122087&date=2019-02-123-Manifold Seminar, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123754&date=2019-02-12
A knot or link $L$ in $S^3$ is called universal if every closed orientable $3$-manifold can be represented as a cover branched over $L$, with some examples including the Borromean rings, the figure-eight knot, and 2-bridge non-torus links. Some such $L$ are the singular locus of an orbifold ${\mathbb H}^3/\Gamma \cong S^3$ for Γ an arithmetic subgroup of the linear algebraic group of isometries of ${\mathbb H}^3$, which gives every closed orientable manifold the structure of an arithmetic orbifold. A natural question, then, is which hyperbolic orbifolds have an arithmetic orbifold group. We will discuss a paper of Hilden-Lozano-Montesinos showing that the orbifold from the $n$-fold cyclic branched cover of the figure-eight knot is arithmetic only at the values $n=4,5,6,8,12,\infty $.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123754&date=2019-02-12Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123673&date=2019-02-12
I will explain the notion of terminal singularities. This is the mildest class of singularities that appears in constructing minimal models of algebraic varieties. In characteristic zero, terminal singularities are automatically Cohen-Macaulay, and this is very useful for the minimal model program. I will present the first known terminal singularity of dimension 3 which is not Cohen-Macaulay; it has characteristic 2. The example is surprisingly easy to describe. Many open problems remain, as I will discuss.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123673&date=2019-02-12Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123674&date=2019-02-12
In this talk I will give a description of the following recent result: the non-Archimedean skeleton of the d-th symmetric power of a smooth projective algebraic curve X is naturally isomorphic to the d-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of X. In the talk I will give all necessary background definitions for understanding the above statement and I will sketch the proof.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123674&date=2019-02-12Harmonic Analysis Seminar, Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123757&date=2019-02-13
Continuation of discussion of “A restriction estimate using polynomial partitioning” by L. Guth. The polynomial partitioning lemma. Construction of the wave packet decomposition and proof of its main properties. $L^2$ bounds for sums of wave packets.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123757&date=2019-02-13Topology Seminar (Introductory Talk), Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123752&date=2019-02-13
I will give a very general overview of lattices in semisimple Lie groups, and a brief introduction to thin groups. This latter class of groups is a current "hot topic", with a plethora of applications to subjects as diverse as number theory, hyperbolic geometry, and quantum computation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123752&date=2019-02-13Large Deviations of Random Projections of High-dimensional Measures, Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123749&date=2019-02-13
Properties of random projections of high-dimensional probability measures are of interest in a variety of fields, including asymptotic convex geometry, and high-dimensional statistics and data analysis. A particular question of interest is to identify what properties of the high-dimensional measure are captured by its lower-dimensional projections. While fluctuations of these projections have been well studied over the past decade, we describe more recent work on both annealed and quenched large deviations principles and associated conditional limit theorems for multidimensional projections. This talk is based on joint works with <br />
<br />
Nina Gantert, Steven Kim and Yin-Ting Liao.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123749&date=2019-02-13Number Theory Seminar, Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123883&date=2019-02-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123883&date=2019-02-13Topology Seminar (Main Talk), Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123753&date=2019-02-13
A celebrated result of Margulis says that among irreducible lattices in higher rank semi-simple Lie groups, arithmetic lattices are characterized as those having dense commensurators. If the subgroup of the Lie group is Zariski dense and discrete but is no longer assumed to have finite covolume (that is, to be thin), then no such definitive dichotomy exists. A heuristic due to Y. Shalom says that thin subgroups should be thought of as non-arithmetic. In this talk I will discuss a theorem confirming Shalom's heuristic for certain naturally defined thin subgroups of \(PSL_2(Z)\). This is joint work with M. Mj.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123753&date=2019-02-13Integrated Analysis of Cancer Data: Multi-omic Clustering and Personalized Ranking of Driver Genes, Feb 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123218&date=2019-02-14
Large biological datasets are currently available, and their analysis has applications to basic science and medicine. While inquiry of each dataset separately often provides insights, integrative analysis may reveal more holistic, systems-level findings. We demonstrate the power of integrated analysis in cancer on two levels: (1) in analysis of one omic in many cancer types together, and (2) in analysis of multiple omics for the same cancer. In both levels we develop novel methods and observe a clear advantage to integration. We also describe a novel method for identifying and ranking driver genes in an individual's tumor and demonstrate its advantage over prior art.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123218&date=2019-02-14Center for Computational Biology and Koret Berkeley Tel Aviv Initiative Seminar, Feb 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123547&date=2019-02-14
Integrated analysis of cancer data: multi-omic clustering and personalized ranking of driver genes<br />
<br />
Abstract: Large biological datasets are currently available, and their analysis has applications to basic science and medicine. While inquiry of each dataset separately often provides insights, integrative analysis may reveal more holistic, systems-level findings. We demonstrate the power of integrated analysis in cancer on two levels: (1) in analysis of one omic in many cancer types together, and (2) in analysis of multiple omics for the same cancer. In both levels we develop novel methods and observe a clear advantage to integration. We also describe a novel method for identifying and ranking driver genes in an individual's tumor and demonstrate its advantage over prior art.<br />
<br />
Biography: Ron Shamir received his PhD from UC Berkeley. He is a Sackler professor of Bioinformatics in the Blavatnik School of Computer Science at Tel Aviv University (TAU). His group develops algorithms in bioinformatics for understanding the genome and human disease. Software tools developed by Shamir’s group are in use around the world. Shamir is the founder and head of the Edmond J. Safra Center for Bioinformatics at TAU. He has published about 300 scientific works, including 17 books and edited volumes, and has supervised more than 50 research students. He was on the founding steering committee of RECOMB, co-founded the Israeli Society of Bioinformatics and Computational Biology, and was society president. He is a recipient of the Landau Prize in Bioinformatics, the Kadar family prize for excellence in research, and a Fellow of the ISCB and the ACM.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123547&date=2019-02-14Mathematics Department Colloquium, Feb 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123591&date=2019-02-14
Consider an algebraic curve in 3-space; when projected generically to a plane, it will acquire a number of double points. This number depends only on the degree and the genus of the curve. Computing similar numbers when the curve is replaced by a surface arbitrarily embedded will be the subject of the lecture. One key difference with the curve case is the fact that we have to work with the Hilbert scheme of k points, instead of the k-th symmetric product, and I will spend some time on the construction of the Hilbert scheme. The main result I will present is the Lehn conjecture, now a theorem, computing all these numbers for all surfaces in terms of their numerical (complex cobordism) invariants.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123591&date=2019-02-14Student Probability/PDE Seminar, Feb 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123869&date=2019-02-15
In this presentation, a classic model known as "small random perturbation of dynamical systems" studied by Freidlin and Wentzell in 1960s is revisited. Freidlin and Wentzell deduced a large-deviation principle for this model, and this result was considerably refined in 2004 by Bovier et. al. In this presentation, we discuss a further refinement of this result via a new technology based on the analysis of suitable Poisson equations. This talk is based on the joint work with F. Rezakhanlou and C. Landim.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123869&date=2019-02-15Beste Basciftci - Value of Optimization under Uncertainty and Integration of Data in Energy Supply Chains, Feb 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122433&date=2019-02-15
Abstract: Most of the real-life problems involve uncertainty, which need to be delicately integrated into the decision-making processes. In this talk, we present various stochastic optimization techniques motivated by maintenance, operations and capacity expansion planning problems in energy systems. In the first part of the talk, our aim is to effectively model and solve the integrated condition-based maintenance and operations scheduling problem of a fleet of generators. We develop a data-driven optimization framework that explicitly considers the effect of the sensor-driven generator failure scenarios and operations schedules on the generators’ degradation levels to construct a reliable and cost-efficient plan. In the second part of the talk, we shift our focus to a more generic problem setting in sequential decision-making under uncertainty. Although two-stage and multi-stage stochastic programming are among the key methodologies to address multi-period problems under uncertainty, they might not provide adequate solutions under limited flexibility by resulting in either fully static or dynamic policies. We propose a novel adaptive stochastic programming approach, in which we optimize the time to revise decisions. We provide theoretical bounds on the performance of the proposed approach compared to the static and dynamic approaches, and present practical implications of the choice of the revision time. We also tailor solution algorithms using our analytical analyses and derive their approximation guarantees. To illustrate our results, we study a generation expansion planning problem demonstrating the advantages of the adaptive approach over existing policies. <br />
<br />
Bio: Beste Basciftci is currently a PhD candidate in Operations Research at the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, with a minor in Statistics. She received her bachelor's degrees in Industrial Engineering and Computer Engineering from Boğaziçi University with High Honors. She also hold a master's degree in Industrial Engineering from Boğaziçi University. She is broadly interested in data-driven decision making problems under uncertainty. Methodologically, her research focuses on developing mixed-integer, stochastic programming and distributionally robust optimization approaches to address operations research/management related problems, specifically for applications in energy, supply chains, production systems, and healthcare operations. Her research also involves developing and integrating statistical modeling and business analytics approaches to the subsequent decision-making processes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122433&date=2019-02-15Student 3-Manifold Seminar, Feb 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123938&date=2019-02-15
A version of the Papakyriakopoulos Sphere Theorem states that a compact $3$-manifold with nontrivial $\pi _2$ has a two-sided embedded sphere or projective plane representing a nontrivial homotopy class. We will discuss ends of groups and how the theorem follows from Stallings's theorem on finitely generated groups with more than one end.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123938&date=2019-02-15Seminar 217, Risk Management: Sustainable Responsible Investing and the Cross-Section of Return and Risk, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122088&date=2019-02-19
The identification of factors that predict the cross-section of stock returns has been a focus of asset pricing theory for decades. We address this challenging problem for both equity performance and risk, the latter through the maximum drawdown measure. We test a variety of regression-based models used in the field of supervised learning including penalized linear regression, tree-based models, and neural networks. Using empirical data in the US market from January 1980 to June 2018, we find that a number of firm characteristics succeed in explaining the cross-sectional variation of active returns and maximum drawdown, and that the latter has substantially better predictability. Non-linear models materially add to the predictive power of linear models. Finally, environmental, social, and governance impact enhances predictive power for non-linear models when the number of variables is reduced.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122088&date=2019-02-19CANCELED: Representation Theory and Mathematical Physics Seminar, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123907&date=2019-02-19
We define the action of infinitely generated Temperley-Lieb algebra on the category of representations of the supergroup \(P(n)\). The supergroup in question is an interesting super analogue of the orthogonal and symplectic groups. As an application of this construction we get algorithm computing characters of irreducible representation of \(P(n)\) and some other esults. As n tends to infinity, we obtain a new universal tensor category equipped with Temperley-Lieb algebra action. In this way we obtain representation of TL in the Fock space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123907&date=2019-02-19Bowen Lectures, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123692&date=2019-02-19
The symmetries of systems of polynomial equations can be be understood in terms of the geometry of the variety of zeroes (or solution set) of the polynomials. Roughly speaking, there are 3 kinds of geometries corresponding to positive, zero and negative curvature giving rise to 3 different kinds of symmetry groups. In this lecture, I will discuss recent advances in algebraic geometry that lead to very precise results on the structure of these symmetry groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123692&date=2019-02-19Harmonic Analysis Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123977&date=2019-02-20
This seminar is an ongoing discussion of Guth's Fourier restriction inequality based on the method of polynomial partitioning. This week's first topic will be a proof of basic properties of the wave packet decomposition. With this machinery in hand, we will begin the core part of the proof, introducing the key concept of broad points, indicating the role of polynomial partitioning, and formulating the inductive step.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123977&date=2019-02-20Topology Seminar (Introductory Talk), Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123354&date=2019-02-20
The Chekanov-Eliashberg algebra is a powerful Legendrian isotopy invariant that is defined by counts of pseudoholomorphic discs. We give an introduction to both analytical and algebraic aspects of the theory, perform calculations in both low and high dimension, and present some open problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123354&date=2019-02-20Algorithmic Pirogov-Sinai theory, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123922&date=2019-02-20
What is the connection between a phase transition in a statistical physics model and the computational complexity of sampling from the given model? In the setting of the hard-core and Potts models on lattices, it is known that in the phase coexistence regime the Glauber dynamics mix slowly. Using some of the same tools used to prove slow mixing (the cluster expansion and Pirogov-Sinai theory), we give efficient algorithms to approximate the partition function of and sample from the hard-core and Potts models at sufficiently low temperatures on the lattice. Our algorithms are inspired by Barvinok's approach to polynomial approximation. Joint work with Tyler Helmuth and Guus Regts.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123922&date=2019-02-20Number Theory Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123974&date=2019-02-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123974&date=2019-02-20Statistics on Shape Data: Correcting an Asymptotic Bias in Template Shape Estimation, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123897&date=2019-02-20
Computational Anatomy aims to model and analyze healthy and pathological distributions of organ shapes. We are interested in the computational representation of the brain anatomy using brain MRIs (Magnetic Resonance Imaging). How can we define the notion of brain shapes and how can we learn their distribution in the population? Landmarks’ shapes, curve shapes or surface shapes can be seen as the remainder after we have filtered out the object position and orientation. As such, shape data belong to quotient spaces. We present “Geometric Statistics”, a framework for data belonging to non-Euclidean spaces like quotient spaces of Riemannian manifolds. We use tools of Geometric Statistics and Riemannian geometry to prove that the “template shape estimation” algorithm, used for more than 15 years in medical imaging (and signal processing), has an asymptotic bias. The geometric intuition provided by the study leads us to design new bias correction methods. We present experimental results on simulated and real data, including a first bias quantification of the brain template computed from MRIs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123897&date=2019-02-20Bowen Lectures, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123693&date=2019-02-20
Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitious program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann Surfaces of genus 0,1 or at least 2 respectively. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123693&date=2019-02-20Special Analysis Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123970&date=2019-02-20
Physical experiments show that interfaces between dissimilar media act as stable channels for the propagation of energy. In discrete models, this stability is explained via an index-like theorem: the bulk edge correspondence. I will first review this principle, which connects the effective number of waves propagating along the interface (a spectral invariant) to a Chern number (a topological invariant).<br />
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I will then focus on a PDE modeling conduction in a graphene layer with a line defect. In a perturbative regime, Fefferman–Lee-Thorp–Weinstein–Zhu constructed waves propagating along the defect. I will show that precisely two of them are topologically stable: they persist outside the perturbative regime. I will then calculate the associated Chern number: it is 2 or -2. These results illustrate the bulk-edge correspondence in a continuous setting.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123970&date=2019-02-20Topology Seminar (Main Talk), Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123319&date=2019-02-20
We use techniques from persistence homology applied to the Chekanov-Eliashberg algebra in order to obtain a restriction on the oscillatory norm of a contact Hamiltonian that displaces a Legendrian in the contact vector space from its image under the Reeb flow. These techniques are also used to show that a Legendrian which admits an augmentation cannot \(C^0\)-approximate a loose Legendrian, and to obstruct the existence of small positive Legendrian loops. This is joint work with M. Sullivan.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123319&date=2019-02-20Applied Math Seminar, Feb 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123967&date=2019-02-21
The Grassmann manifold Gr(m,n) is the set of n-dimensional subspaces in $\mathbb R^m$ (assuming m >n), and is used in many science and engineering applications. A point in Gr(m,n) can be represented by an orthogonal matrix of size m by n, multiplied by another arbitrary orthogonal matrix of size n by n. In quantum chemistry and in particular the widely used density functional theory (DFT), this arbitrary orthogonal matrix is referred to as the gauge. Physical quantities such as energies and electron densities should be independent of the gauge choice. In this talk, I am going to discuss the interplay between gauge-dependent and gauge-independent quantities in quantum chemistry along three recent directions: time-dependent density functional theory, electron localization, and self-consistent field iteration. In each case, the focus on the gauge-independent representation of the Grassmann manifold brings interesting, and sometimes surprising numerical benefits.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123967&date=2019-02-21Mathematics Department Colloquium/Bowen Lectures, Feb 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123694&date=2019-02-21
After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by $p_1,...,p_r$ in $C[x_1,...,x_n]$) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic $p >0$. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic $p >5$ by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123694&date=2019-02-21Student Probability/PDE Seminar, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123976&date=2019-02-22
I will talk about several different perspectives to analyze the structure of Gibbs measures with low complexity. The first perspective is a mean-field approximation to the free energy that appears in the variational formula, studied by Chatterjee and Dembo. As an application, one can compute the probability of large deviation events given by nonlinear functions with low complexity, for instance counting the number of subgraphs of the Erdos-Renyi random graphs in the sparse regime. Another direction is studied by Eldan, which says that Gibbs measure is approximately close to the mixture of product measures with an error term expressed in terms of the 'Gaussian-width gradient complexity'. The another possible method is recently introduced by Austin, which is based on purely information theoretical techniques. I will briefly mention these methods and discuss the strength of each perspective and relations between them.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123976&date=2019-02-22Logic Colloquium, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123724&date=2019-02-22
The discovery of non euclidean geometry in the early nineteenth century had shaken the beliefs and conjectures of more than two thousand years and changed the picture we had for mathematics, physics and even philosophy. Lobachevsky and Bolyai independently around 1830 discovered hyperbolic geometry. A notable distinguish feature of hyperbolic geometry is its negative curvature in a way that the sum of angles of a triangle is less than π. Gromov much later in 1987 introduced hyperbolic groups which are groups acting "nicely" on hyperbolic spaces, or equivalently finitely generated groups whose Cayley graphs are "negatively curved". Main examples are free groups and almost all surface groups. The fascinating subject of hyperbolic groups touches on many mathematical disciplines such as geometric group theory, low dimensional topology and combinatorial group theory. It is connected to model theory through a question of Tarski.<br />
<br />
Tarski asked around 1946 whether non abelian free groups have the same common first order theory. This question proved extremely hard to answer and only after more than fifty years in 2001 Sela and Kharlampovich-Myasnikov answered it positively. Both works are voluminous and have not been absorbed yet. The techniques almost exclusively come from the disciplines mentioned above, hence it is no wonder that the question had to wait for their development. The great novelty of the methods and the depth of the needed results have made it hard to streamline any of the proofs. Despite the difficulties there is some considerable progress in the understanding of the first order theory of "the free group" and consequently first order theories of hyperbolic groups from the scopes of basic model theory, Shela's classification theory and geometric stability. In this talk I will survey what is known about these theories and what are the main open questions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123724&date=2019-02-22Student 3-Manifold Seminar, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124151&date=2019-02-22
This is a continuation of last week's talk about Stalling's work on ends of groups, with the Sphere Theorem as an application.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124151&date=2019-02-22Combinatorics Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123672&date=2019-02-25
We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al.. This characterization is a combination of local queer axioms generalizing Stembridge's local axioms for crystal bases for simply-laced root systems, which were recently introduced by Assaf and Oguz, with further axioms and a new graph $G$ characterizing the relations of the type $A$ components of the queer crystal. We provide a counterexample to Assaf's and Oguz' conjecture that the local queer axioms uniquely characterize the queer supercrystal. We obtain a combinatorial description of the graph $G$ on the type $A$ components by providing explicit combinatorial rules for the odd queer operators on certain highest weight elements.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123672&date=2019-02-25Probabilistic Operator Algebra Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122911&date=2019-02-25
Consider a quantum system consisting of N particles, and assume that it is in a random pure state (i.e., uniform over the sphere of the corresponding Hilbert space H). Let A and B be two subsystems consisting of k particles each. Then there exists a threshold value $k_0 \sim N/5$ such that<br />
<br />
(i) if $k > k_0$, then A and B typically share entanglement<br />
<br />
(ii) if $k < k_0$, then A and B typically do not share entanglement.<br />
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We give precise statements of results of the above type and outline the arguments which involve random matrices, majorization, and various concepts/techniques from geometric functional analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122911&date=2019-02-25String-Math Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123213&date=2019-02-25
Virasoro constraints are omnipresent in enumerative geometry. Recently, Kontsevich and Soibelman introduced a generalization of Virasoro constraints in the form of Airy structures. It can also be understood as an abstract framework underlying the topological recursion of Chekhov, Eynard and Orantin. In this talk I will explain how the triumvirate of Virasoro constraints, Airy structures and topological recursion can be generalized to W-algebra constraints, higher Airy structures and higher topological recursion. I will briefly discuss the enumerative geometric meaning of the resulting W-constraints in the context of open and closed intersection theory on the moduli spaces or curves with r-spin structure and its variants.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123213&date=2019-02-25Arithmetic Geometry and Number Theory RTG Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123755&date=2019-02-25
The Breuil-Mezard conjecture predicts the geometry of local Galois deformation rings with p-adic Hodge theory condition in terms of modular representation theory. I will begin by reformulating this conjecture in terms of the Emerton-Gee moduli stack of mod p Galois representations. I will then describe joint work in progress with Daniel Le, Bao V. Le Hung, and Stefano Morra where we prove the conjecture in generic situations for a class of potentially crystalline deformation rings. The key ingredient is the construction of a local model which models the singularities of these Galois deformation rings.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123755&date=2019-02-25Nonlinear Algebra Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123870&date=2019-02-25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123870&date=2019-02-25Privately Learning High-Dimensional Distributions, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124058&date=2019-02-25
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian in R^d and learning a product distribution in {0,1}^d in total variation distance. The sample complexity of our algorithms nearly matches the sample complexity of the optimal non-private learners for these tasks in a wide range of parameters. Thus, our results show that private comes essentially for free for these problems, providing a counterpoint to the many negative results showing that privacy is often costly in high dimensions. Our algorithms introduce a novel technical approach to reducing the sensitivity of the estimation procedure that we call recursive private preconditioning, which may find additional applications. Based on joint work with Jerry Li, Vikrant Singhal, and Jonathan Ullman.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124058&date=2019-02-25Differential Geometry Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123671&date=2019-02-25
We show that a Ricci flow in four dimensions can develop singularities modeled on the Eguchi-Hanson space. In particular, we prove that starting from a class of asymptotically cylindrical $U(2)$-invariant initial metrics on $TS^2$, a Type II singularity modeled on the Eguchi-Hanson space develops in finite time. Furthermore we show that in our setup blow-up limits at larger scales are isometric to either (i) the flat $\mathbb R^4 /\mathbb Z_2$ orbifold, (ii) a rotationally symmetric, positively curved, asymptotically cylindrical ancient orbifold Ricci flow on $\mathbb R^4/\mathbb Z_2$, or (iii) the shrinking soliton on $\mathbb R \times \mathbb R P^3$. As a byproduct of our work, we also prove the existence of a new family of Type II singularities caused by the collapse of a two-sphere of self-intersection $|k| \geq 3$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123671&date=2019-02-25Nonlinear Algebra Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123871&date=2019-02-25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123871&date=2019-02-25Seminar 217, Risk Management: Collateralized Networks, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122089&date=2019-02-26
We study the spread of losses and defaults through financial networks focusing on two important elements of regulatory reforms: collateral requirements and bankruptcy stay rules in over-the-counter (OTC) markets. Under "segregated" collateral requirements, one firm can benefit from the failure of another, the failure frees the committed collateral of the surviving firm giving it additional resources to make other payments. In OTC derivatives markets, similarly, one firm may obtain additional resources upon the failure of another if it terminates its in the money derivatives with the failed entity. Studying contagion in the presence of this real world phenomenon becomes challenging. Our proposed model deviates from the existing network models to capture collateral and accelerated contract termination payments. The model also incorporates fire sales externalities when collateral is held in illiquid assets. We show that asset fire sales increase the risk of contagion if illiquid collateral is seized and sold immediately upon defaults. We also analyze the impact of different bankruptcy stay rules on contagion. Some of our results contrast with the post-crisis stay rules. For instance, we show that when banks are not highly leveraged in terms of their OTC derivatives transactions, which is now the case due to the impact of regulatory reforms, symmetric contract termination in the absence of automatic stays can reduce the risk of contagion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122089&date=2019-02-26Student Harmonic Analysis and PDE Seminar (HADES), Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123942&date=2019-02-26
Concentration compactness methods provide a powerful tool for proving global well-posedness and scattering for nonlinear dispersive equations. Once one has a small-data global well-posedness result, one knows that there is some minimal size of the initial data at which global well-posedness and scattering can fail. Then, using a profile decomposition, one can show that there is a minimal blowup solution that is almost periodic. One can then use tools like long-time Strichartz estimates and interaction Morawetz inequalities to rule out these "minimal enemies." I will illustrate this technique by presenting a proof, due to Killip and Visan, of the global well-posedness and scattering for the three-dimensional energy-critical defocusing NLS.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123942&date=2019-02-263-Manifold Seminar, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124188&date=2019-02-26
It is a natural idea to try to distinguish finitely generated groups via their finite quotients. To do that, we restrict to the class of residually finite groups and study their profinite completions. We will discuss these concepts and their relation to separable subgroups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124188&date=2019-02-26Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123751&date=2019-02-26
Codepth is the dual notion to depth, being the greatest length of a coregular sequence for a module, meaning the first element maps the module surjectively, the second is subjective on the kernel of the first, and so on. For a curve in P3, let M be the local cohomology module of the graded coordinate ring with supports in the ideal of the curve. Then the theorem of Hellus says that C is a set theoretic complete intersection if and only if M has codepth 2. This criterion is not directly applicable, so we define the notion of a quasi-cyclic module, which is an increasing limit of cyclic modules. In this talk I will recall the still open problem of whether every irreducible nonsingular curve in P3 is a set theoretic complete intersection, and derive a number of consequences using the concepts introduced above.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123751&date=2019-02-26Representation Theory and Mathematical Physics Seminar, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124185&date=2019-02-26
The talk will start with a reminder of what is a Hamiltonian integrable system and what degenerate integrability, also know as superintegrability, means. Then examples of such systems on symplectic leaves of Poisson variety \(K\backslash T^*G/K\) will be constructed for a Lie group \(G\) and a Lie subgroup \(K\subset G\). If \(G\) is a simple Lie group and \(K\) is the subgroup of fixed points of the Chevalley automorphism of \(G\), Hamiltonians of such integrable systems will be described explicitly.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124185&date=2019-02-26Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124186&date=2019-02-26
We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial and verify its log-concavity, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on the log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124186&date=2019-02-26Harmonic Analysis Seminar, Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124189&date=2019-02-27
This seminar is an ongoing discussion of Guth's Fourier restriction inequality based on the method of polynomial partitioning. This week's talk continues discussion of the core part of the proof, utilizing the key concept of broad points to carry out the inductive step. Following the incidence problem model, the analysis divides into three parts. A key decomposition, including a bilinear term, will be introduced.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124189&date=2019-02-27Topology Seminar (Introductory Talk), Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124183&date=2019-02-27
I'll define hyperbolic group, relatively hyperbolic group, the boundary, and give examples and basic properties.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124183&date=2019-02-27Deformation Theory Seminar, Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124267&date=2019-02-27
I will review the appearance of curvings for objects in the deformation theory of categories and discuss conditions for their removal. I will review the role of nilpotence in reduction to uncurved deformations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124267&date=2019-02-27Statistical Physics, Markov Chains, and Programmable Matter, Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124066&date=2019-02-27
I will discuss how tools from statistical physics used to analyze partition functions, such as Peierls arguments and the cluster expansion, can be used to solve seemingly unrelated distributed computing problems about programmable matter. Programmable matter is a material or substance that has the ability to change its features in a programmable, distributed way; examples are diverse and include robot swarms and smart materials. We study an abstraction of programmable matter where particles independently move on a lattice according to simple, local algorithms. We want to design these algorithms so that the system has a desired collective behavior, such as compression of the particles into a shape with small perimeter or separation of differently colored particles. In our stochastic approach, we describe a desired collective behavior using an energy function; design a Markov chain that uses local moves and converges to the Gibbs distribution for this energy function; and then turn the Markov chain into an asynchronous distributed algorithm that each particle can execute independently. To prove our algorithms are correct, we must show this Gibbs distribution has the desired properties with high probability. Our previous work on the compression problem used Peierls arguments to analyze the Gibbs distribution. More recent work on the separation problem necessitated the introduction of the cluster expansion to analyze the Gibbs distribution. The key feature of the cluster expansion we use is that we can separate partition functions into volume and surface terms that we can deal with separately. Joint work with Joshua J. Daymude, Cem Gokmen, Dana Randall, and Andrea Richa.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124066&date=2019-02-27Number Theory Seminar, Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124182&date=2019-02-27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124182&date=2019-02-27Mean Estimation with Sub-Gaussian Rates in Polynomial Time, Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124133&date=2019-02-27
We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector X has finite mean and covariance. In this setting, the radius of confidence intervals achieved by the empirical mean are large compared to the case that X is Gaussian or sub-Gaussian.<br />
We offer the first polynomial time algorithm to estimate the mean with sub-Gaussian-size confidence intervals under such mild assumptions. Our algorithm is based on a new semidefinite programming relaxation of a high-dimensional median. Previous estimators which assumed only existence of finitely-many moments of X either sacrifice sub-Gaussian performance or (as with recent breakthrough work by Lugosi and Mendelson, 2019) are only known to be computable via brute-force search procedures requiring time exponential in the dimension.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124133&date=2019-02-27Topology Seminar (Main Talk), Feb 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124184&date=2019-02-27
I'll survey what is known about the way the boundary of a relatively hyperbolic group is affected by relatively hyperbolic Dehn filling. I'll talk both about geometric and algebraic topological properties of the boundary. Parts of this talk will be based on joint works with Groves, Groves–Sisto, and Wang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124184&date=2019-02-27Mathematics Department Colloquium, Feb 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124263&date=2019-02-28
Discrete subgroups of Lie groups play a fundamental role in several areas of mathematics. Discrete subgroups of $SL(2,\mathbb R)$ are well understood, and classified by the geometry of the corresponding hyperbolic surfaces. On the other hand, discrete subgroups of $SL(n,\mathbb R)$ for $n >2$, beyond lattices, remain quite mysterious. While lattices in this setting are rigid, there also exist more flexible "thinner" discrete subgroups, which may have large and interesting deformation spaces (some of them with topological and geometric analogies to the Teichmüller space of a surface, giving rise to so-called "higher Teichmüller theory"). We will survey recent progress in constructing and understanding such discrete subgroups from a geometric and dynamical viewpoint.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124263&date=2019-02-28Student Probability/PDE Seminar, Mar 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123743&date=2019-03-01
This is joint work with Martin Hairer, Gautam Iyer, Leonid Koralov, and Zsolt Pajor-Gyulai. This work studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that start close enough to cell boundaries is a fractional kinetic process: A Brownian motion time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell framework, and the key step is to establish an analogous averaging principle on shorter time scales. As a consequence of our main theorem, we obtain a homogenization result for the associated advection-diffusion equation. We show that on intermediate time scales the effective equation is a fractional time PDE that arises in modelling anomalous diffusion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123743&date=2019-03-01Student 3-Manifold Seminar, Mar 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124325&date=2019-03-01
The irreducible 3-manifolds that come from a prime decomposition can be further decomposed along embedded tori. Jaco, Shalen, and Johannson proved there is a minimal collection of such tori, unique up to isotopy, that splits an irreducible compact orientable manifold into pieces that are either Seifert-fibered or atoroidal. We will discuss examples, incompressible surfaces, and Seifert-fibered spaces.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124325&date=2019-03-01Student Arithmetic Geometry Seminar, Mar 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124302&date=2019-03-01
Toric varieties are varieties with an action of a torus having an open orbit. Spherical varieties are natural generalizations, having an action of reductive group with an open Borel orbit. Like with toric varieties, there are natural combinatorial invariants that one can define from a spherical variety, such as the irreducible summands which appear in the ring of regular functions. Losev proved that, for the case of (smooth) affine spherical varieties and the case of homogeneous spherical varieties, these combinatorial invariants uniquely determine the variety with the G-action.<br />
<br />
We will define spherical varieties and the combinatorial invariants involved, giving examples. Then we'll state the theorems due to Losev. Time permitting, we'll also discuss some ideas of the proof, along with other results related to these theorems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124302&date=2019-03-01Combinatorics Seminar, Mar 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124301&date=2019-03-04
For finite dimensional representations $V_1, \dots , V_m$ of a simple finite dimensional Lie algebra $\mathfrak g$ consider the tensor product $W=\otimes _{I=1}^m V_i^{\otimes N_i}$. The first result, which will be presented in the talk, is the asymptotic of the multiplicity of an irreducible representation $V_\lambda $ with the highest weight λ in this tensor product when $N_i=\tau _i/\epsilon , \lambda =\xi /\epsilon $ and $\epsilon \to 0$. Then we will discuss the asymptotical distribution of irreducible components with respect to the character probability measure $Prob(\lambda )=\frac {m_\lambda \chi _{V_\lambda }(e^t)}{\chi _W(e^t)}$. Here $\chi _V(e^t)$ is the character of representation $V$ evaluated on $e^t$ where $t$ is an element of the Cartan subalgebra of the split real form of the Lie algebra $\mathfrak g$. This is a joint work with O. Postnova.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124301&date=2019-03-04JUNIPR: a framework for unsupervised and interpretable machine learning in particle physics, Mar 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124348&date=2019-03-04
In applications of machine learning to particle physics, a persistent challenge is how to go beyond discrimination to learn about the underlying physics. In this talk, we will present a new framework: JUNIPR, Jets from UNsupervised Interpretable PRobabilistic models, which uses unsupervised learning to learn the intricate high-dimensional contours of the data upon which it is trained, without reference to pre-established labels. In order to approach such a complex task, JUNIPR is structured intelligently around a leading-order model of the physics underlying the data. In addition to making unsupervised learning tractable, this design actually alleviates existing tensions between performance and interpretability. Applications to discrimination, data-driven Monte Carlo generation and reweighting of events will be discussed. Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
<br />
The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124348&date=2019-03-04Arithmetic Geometry and Number Theory RTG Seminar, Mar 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123884&date=2019-03-04
After reviewing Siegel-Weil formula and progress on arithmetic Siegel-Weil formula, I will talk about my new work with Jan Bruinier on this subject. Let $L$ be an integral lattice of signature $(n, 2)$ over $\mathbb Q$, and let $T$ be a non-singular symmetric integral matrix. Associated to it are two objects. One is the $T$-th Fourier coefficient $a(T)$ of the derivative of some `incoherent’ Siegel Eisenstein series. The other one is an arithmetic $0$ divisor $\widehat{\mathcal Z}(T)$, which can only be supported at one prime (including $\infty$). The arithmetic Siegel-Weil formula claims that $a(T)$ is equal to the degree of the arithmetic $0$-divisor $\widehat{\mathcal Z}(T)$. In this joint work, we proved that it is true when the support is at $\infty$ or at prime $p$ when $L$ is unimodular and $\mathcal Z(T)(\bar{\mathbb F}_P)$ is finite. I should mention that Garcia and Sankaran have a very different proof when the support is at the infinity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123884&date=2019-03-04Reproducing AlphaZero: what we learn, Mar 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124059&date=2019-03-04
We reproduce and open source AlphaGoZero/AlphaZero framework using 2000 GPUs and 9 days, achieving super-human performance of Go AI that beats 4 top-30 professional players with 20-0, provide extensive ablation studies and perform basic analysis. In this talk we will share our journey and interesting first-hand experience that makes a large-scale RL system work. We hope it will spur future research both practically and theoretically.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124059&date=2019-03-04Analysis and PDE Seminar, Mar 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124387&date=2019-03-04
We consider the Korteweg-de Vries (KdV) equation, and prove that small localized data yields solutions which have dispersive decay on a quartic time-scale. This result is optimal, in view of the emergence of solitons at quartic time, as predicted by inverse scattering theory. Joint work with Herbert Koch and Daniel Tataru.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124387&date=2019-03-04Seminar 217, Risk Management: How elementary is diversification?, Mar 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122090&date=2019-03-05
Diversification is a fundamental concept in financial economics, risk management, and decision theory. From a broad perspective, it conveys the idea of introducing variety to a set of objects. Today, there is general consensus that some form of diversification is beneficial in asset allocation, however its definition is context-dependent and there is no consensus on a widely accepted, mathematically concise and economically sound notion of diversification. Indeed, there is an ongoing debate about what the “best” level of diversification should be. There is also a recent trend of evaluating certain diversifying heuristics as being “anomalous” and “irrational”. In this talk, I shall approach the notion of diversification from a foundational perspective by asking how elementary it really is. I take the view that diversification is a behavioural choice heuristic and an evolutionary cognitive adaptation that is selectively advantageous under many economic and financial circumstances. The talk will dig deeper into the roots of this paradigm; first, through an experimental study on children that looks into whether they would diversify in a sequence of gambles aimed at replicating typical portfolio choice scenarios; then by formulating an evolutionary theory of diversification.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122090&date=2019-03-053-Manifold Seminar, Mar 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124386&date=2019-03-05
We'll discuss quasiconvex subgroups of fundamental groups of special cube complexes. These give rise to isometrically immersed complexes with separable fundamental group, proving that quasiconvex subgroups are separable.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124386&date=2019-03-05Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Mar 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124187&date=2019-03-05
We describe the nef cone of the toric variety corresponding to a Coxeter complex. Equivalently, this is the cone of deformations of a Coxeter permutahedron. This family contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra and submodular functions to any finite reflection group. This is joint work with Federico Castillo, Chris Eur, and Alex Postnikov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124187&date=2019-03-05Harmonic Analysis Seminar, Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124467&date=2019-03-06
This seminar is an ongoing discussion of Guth's Fourier restriction inequality based on the method of polynomial partitioning. This week's talk continues discussion of the core part of the proof. The structure of the induction — on the radius and on the $L^2$ norm of $f$, applied to the cellular term — will be presented. Insofar as time allows, the tranverse and tangential terms will be analyzed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124467&date=2019-03-06Topology Seminar (Introductory Talk), Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124417&date=2019-03-06
We will introduce Scharlemann-Thompson handle decompositions of a 3-manifold, and a generalization of this which we call a graph decomposition. Using these, we define topological measures of complexity for the manifold. In the case where the manifold has additional metric structure, we use Morse and Morse-like functions to give geometric definitions of complexity as well. We then show that some of these geometric and topological complexities are linearly related for hyperbolic 3-manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124417&date=2019-03-06Deformation Theory Seminar, Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124370&date=2019-03-06
We will construct deformations of categories for Hochschild Maurer-Cartan cochains with non-trivial curving components. These will be related to fixed point categories for Lie algebra actions and, in the special case of matrix factorizations, to the category of singularitieshttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124370&date=2019-03-06Triangular" Dvoretzky matrices and online coding, Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124373&date=2019-03-06
A special case of the classical Dvoretzky theorem states that the space of n-dimensional real vectors equipped with the l1 norm admits a large "Euclidean section", i.e. a subspace of dimension Θ(n) on which a scaled l1 norm essentially agrees with the Euclidean norm. In particular, such a subspace can be realized as the column space of a "tall" n × (n/k) random matrix A with identically distributed independent Gaussian entries (k > 1).<br />
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This special case of the Dvoretzky theorem has a natural interpretation in the setting of encoding real vectors for transmission across an adversarial noisy channel when the vector x to be encoded is given in advance (the so-called "block coding" scenario), so that the encoding can be computed in an "offline" fashion. Motivated by the same problem in the setting when the encoding has to be "online", i.e., has to be carried out as each entry of x becomes available, we give randomized constructions of triangular matrices with properties similar to Dvoretzky matrices. The guarantees provided by these constructions in the "online" scenario are close to, but still somewhat worse than, those provided by the Dvoretzky theorem in the "block" scenario, and the question of finding the optimal triangular version of the Dvoretzky theorem remains open.<br />
<br />
Joint work with Leonard J. Schulman.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124373&date=2019-03-06Towards honest inference from real-world healthcare data, Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124169&date=2019-03-06
In practice, our learning healthcare system relies primarily on observational studies generating<br />
one effect estimate at a time using customized study designs with unknown operating<br />
characteristics and publishing – or not – one estimate at a time. When we investigate<br />
the distribution of estimates that this process has produced, we see clear evidence<br />
of its shortcomings, including an apparent over-abundance of statistically significant effects.<br />
We propose a standardized process for performing observational research that<br />
can be evaluated, calibrated and applied at scale to generate a more reliable and complete<br />
evidence base than previously possible. We demonstrate this new paradigm by generating <br />
evidence about all pairwise comparisons of 39 treatments for hypertension for a relevant <br />
set of 58 health outcomes using nine large-scale health record databases from four countries. <br />
In total, we estimate 1.3M hazard ratios, each using a comparative effectiveness study <br />
design and propensity score stratification on par with current one-off observational studies <br />
in the literature. Moreover, the process enables us to employ negative and positive controls <br />
to evaluate and calibrate estimates ensuring, for example, that the 95% confidence <br />
interval includes the true effect size 95% of time. The result set consistently reflects <br />
current established knowledge where known, and its distribution shows no evidence <br />
of the faults of the current process.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124169&date=2019-03-06Topology Seminar (Main Talk), Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124418&date=2019-03-06
We will introduce Scharlemann-Thompson handle decompositions of a 3-manifold, and a generalization of this which we call a graph decomposition. Using these, we define topological measures of complexity for the manifold. In the case where the manifold has additional metric structure, we use Morse and Morse-like functions to give geometric definitions of complexity as well. We then show that some of these geometric and topological complexities are linearly related for hyperbolic 3-manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124418&date=2019-03-06Center for Computational Biology Seminar, Mar 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120948&date=2019-03-06
Large-scale genomic data reveal mechanisms of mutagenesis and help predict complex phenotypes<br />
<br />
Abstract:<br />
Statistical analysis of large genomic datasets has recently emerged as a discovery tool in many areas of genetics. Two examples include studies of mutagenesis and of the relationship between genotype and phenotype. We developed a statistical model of regional variation of human mutation rate. Application of this model to population sequencing data generated strong mechanistic hypotheses on the origin of human mutation. In a separate study, we developed a method that predicts complex phenotypes, such as common human diseases, from genotypes. This new non-parametric shrinkage (NPS) method does not make any specific assumptions regarding allelic architecture. The method reliably corrects for linkage disequilibrium in summary statistics of 5 million dense genome-wide markers and consistently improves prediction accuracy over state of the art techniques.<br />
<br />
Biography:<br />
Shamil Sunyaev is a computational genomicist and geneticist. Research in his lab encompasses many aspects of population genetic variation including the origin of mutations, the effect of allelic variants on molecular function, population and evolutionary genetics, and genetics of human complex and Mendelian traits. He developed several computational and statistical methods widely adopted by the community. Sunyaev obtained a PhD in molecular biophysics from the Moscow Institute of Physics and Technology and completed his postdoctoral training in bioinformatics at the European Molecular Biology Laboratory (EMBL). He is an Associate Member at Broad Institute of MIT and Harvard.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120948&date=2019-03-06Applied Math Seminar, Mar 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123356&date=2019-03-07
We characterize the intrinsic complexity of a set in a metric space by the least dimension of a linear space that can approximate the set to a given tolerance. This is dual to the characterization using Kolmogorov n-width, the distance from the set to the best n-dimensional linear space. We study the approximation of random vectors (via principal component analysis a.k.a. singular value decomposition) and random fields (via Karhunen– Loève expansion) as well as the approximate separability of the Green’s function of the Helmholtz equation for high frequency waves. We provide lower bounds and upper bounds for the intrinsic complexity and its asymptotic scaling law.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123356&date=2019-03-07Close-Kin Genetic Methods to Infer Demography and Dispersal Patterns of Mosquitoes, Mar 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124423&date=2019-03-07
Malaria, dengue, Zika and other mosquito-borne diseases continue to pose a major global health burden through much of the world, despite the widespread distribution of insecticide-based tools and antimalarial drugs. Consequently, there is interest in novel strategies to control these diseases, including the release of mosquitoes transfected with Wolbachia and engineered with CRISPR-based gene drive and disease-refractory systems. The safety and effectiveness of these strategies are critically dependent on a detailed understanding of mosquito demography and movement patterns at both fine and broad spatial scales, yet there are major gaps in our understanding of these. The declining cost of genome sequencing and novel methods for analyzing geocoded genomic data provide opportunities to address these knowledge gaps. In this talk, we discuss a new approach to infer fine-scale mosquito dispersal patterns and demographic parameters, such as population size and mating structure, by considering the information contained in a set of pairs of closely-related individuals whose locations are known. These methods have previously been applied to fish such as tuna, sharks and coral trout; but have not yet been applied to insects. We propose in silico simulations of mosquito ecology and dispersal to determine sampling routines capable of quantifying known dispersal patterns and demographic parameters. The resulting models will be used to explore the potential impact of novel mosquito control interventions, and to inform biosafety and trial design considerations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124423&date=2019-03-07Mathematics Department Colloquium, Mar 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124419&date=2019-03-07
In their influential series of papers in the 90's, Kazhdan and Lusztig established an equivalence between the category of G(O)-integrable representations of the Kac-Moody Lie algebra and the category of modules over the "big" (i.e., Lusztig's) quantum group. In this talk we will explain what happens if we try to describe in terms of the quantum group the full affine category O. We will also connect this with quantum Langands duality and factorizable sheaves.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124419&date=2019-03-07Student Probability/PDE Seminar, Mar 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124421&date=2019-03-08
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124421&date=2019-03-08Student 3-Manifold Seminar, Mar 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124524&date=2019-03-08
This is a continuation of last week's talk. We will discuss Seifert-fibered spaces and the existence of JSJ decompositions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124524&date=2019-03-08Combinatorics Seminar, Mar 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124420&date=2019-03-11
In this talk I will introduce an interesting connection between the theory of Hopf monoids in combinatorics and Mobius inversion. Roughly, a Hopf monoid is an algebraic abstraction of families of combinatorial objects which have an operation which combines objects and an operation which breaks objects apart. Like many algebraic structures, Hopf monoids have a nice notion of duality. We will show that for many combinatorial families, this notion of duality can be interpreted as Mobius inversion in an appropriate poset. We will focus on the examples of symmetric functions, graphs, and scheduling problems. No previous knowledge of Hopf monoids will be assumed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124420&date=2019-03-11String-Math Seminar, Mar 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124544&date=2019-03-11
This is a joint work with A. Oblomkov exploring the relation between the HOMFLY-PT link homology and coherent sheaves over the Hilbert scheme of points on \(\mathbb C^2\).<br />
<br />
We consider a special object in the 2-category related to the Hilbert scheme of n points on \(\mathbb C^2\). We define a homomorphism from the braid group on n strands to the monoidal category of endomorphisms of this object. We prove that the space of morphisms between the images of a braid and of the identity braid is the invariant of a link constructed by closing the braid. Conjecturally, this space is the triply-graded HOMFLY-PT homology.<br />
<br />
From the TQFT point of view, we consider a B-twisted \(3d\) \(N=4\) SUSY YM with matter, whose Higgs branch is the Hilbert scheme.<br />
<br />
Link homology appears as the Hilbert space of a 2-disk. Its boundary carries a flag variety-based sigma model, and the Kahler parameters of the flag variety braid as one goes around the disk.<br />
<br />
From the IIA string theory point of view, the points on \(\mathbb C^2\) are BPS particles coming from a 2-disk shaped stack of n D2-branes located in one of the fibers at the North Pole of \(\mathbb P^1\), which forms the base of a resolved conifold. The D2-branes end on a stack of NS5 branes which form a closed braid in the other fiber.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124544&date=2019-03-11Arithmetic Geometry and Number Theory RTG Seminar, Mar 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123756&date=2019-03-11
(1) De Rham-Witt: review and prospects. (2) Remarks on the cotangent complex and the Nygaard filtration. I'll discuss some well known relations between the cotangent complex, liftings mod $p^2$, and the de Rham-Witt complex.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123756&date=2019-03-11Differential Geometry Seminar, Mar 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124537&date=2019-03-11
I will describe some results concerning Kähler-Ricci solitons. This is joint work with Alix Deruelle and Song Sun.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124537&date=2019-03-11Seminar 217, Risk Management: Financial Frictions, Foreign Currency Borrowing, and Systemic Risk, Mar 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122091&date=2019-03-12
We present a novel explanation for the prevalence of foreign-currency borrowing in emerging markets. First, under limited liability, foreign-currency denominated debt acts as a state-contingent claim: Borrowers maximizing profits in local currency are partly shielded from large devaluations through bankruptcy, when repaying foreign currency debt is expensive, but pay higher rates in non-devaluation states, when repayment is relatively cheaper. Second, foreign- currency borrowing can improve firms’ incentives and reduce agency problems at the cost of higher systemic risk. The resulting trade-off between average performance and systemic stability, which becomes stronger when bankruptcies entail externalities, lends support to regulation limiting currency mismatches.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122091&date=2019-03-12Student Harmonic Analysis and PDE Seminar (HADES), Mar 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124541&date=2019-03-12
In this talk, I will present a proof of global existence of solutions to certain quasilinear wave equations in three space dimensions with small initial data. The talk is based on a paper by Hans Lindblad published in 2008.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124541&date=2019-03-123-Manifold Seminar, Mar 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124557&date=2019-03-12
We’ll introduce some preliminaries such as Hodge theory and spin structure for Seiberg-Witten invariants on 4-manifolds. Then a nice nonlinear PDE on the spin bundle of 4-manifolds will give rise to a moduli space related to Seiberg-Witten invariants. We will also discuss some related results of hyperbolic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124557&date=2019-03-12Chern Lectures, Mar 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124303&date=2019-03-12
We will discuss the longstanding bi-Lipschitz embedding problem in $\mathbb R^k$, and how over the years it became intertwined with the embeddability properties of the Heisenberg groups into $L_p(\mu )$ spaces. We will explain a recent completion of this project, which exhibits unexpected twists, decisive applications to longstanding open questions in algorithms and metric geometry, and connections to subtle structural issues in analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124303&date=2019-03-12Harmonic Analysis Seminar, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124543&date=2019-03-13
This is a continuation of an ongoing discussion of Guth's Fourier restriction inequality, based on the method of polynomial partitioning. This week's talk focuses on the bilinear term that arises in controlling the contribution of tubes that are roughly tangential to cell walls. The concept of broad points finally pays its dividend.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124543&date=2019-03-13Bay Area Microlocal Analysis Seminar, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124465&date=2019-03-13
Kapustin and Witten introduced a new set of gauge-theoretic equations, which were later proposed by Gaiotto and Witten as a tool to access some old and new manifold invariants. I will describe recent progress on the analytic foundations of this subject. Joint work with Witten and with S. He.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124465&date=2019-03-13Topology Seminar (Introductory Talk), Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124521&date=2019-03-13
The evasion path problem asks: Given a finite collection of sensors continuously moving in a bounded domain in \(\mathbb R^n\) for a finite length of time, such that each sensor can detect the presence of objects in a ball of fixed radius around itself, when can an intruder in the domain avoid being detected for the full length of time? The continuous path that such an intruder takes is called an evasion path, and the question asks about existence of an evasion path. We describe prior results on this problem by da Silva-Ghrist, Adams-Carlsson, and Ghrist-Krishnan, focusing in particular on the necessary condition for existence of an evasion path provided by Adams-Carlsson and based on zig-zag persistent homology of the time-varying Cech complex. We will first review persistent homology and zig-zag persistence.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124521&date=2019-03-13Deformation Theory Seminar, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124584&date=2019-03-13
We will discuss the notion of partitioned Lie algebras, which gives the characteristic $p$ notion of a Lie algebra that is suited to formal deformation theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124584&date=2019-03-13Correlation Length in the Near-Critical Planar Ising Model, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124505&date=2019-03-13
I will discuss joint work with Federico Camia and Jianping<br />
Jiang (arXiv:1707.02668) which proves exponential decay of correlations<br />
for the generalized random field that is the scaling limit of the<br />
near-critical (i.e., with small magnetic field at the critical<br />
temperature) two-dimensional Ising model. The proof involves<br />
both lattice and continuum FK (Fortuin-Kasteleyn) representations<br />
of the Ising model and the use<br />
of coupled conformal loop and measure ensembles.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124505&date=2019-03-13Bay Area Microlocal Analysis Seminar, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123975&date=2019-03-13
I will discuss the geometric inverse problem of recovering a connection from the parallel transport along geodesics of a compact Riemannian manifold with strictly convex boundary or along light rays in Minkowski space. This problem is motivated by other geometric inverse problems and is tackled with a range of techniques including energy estimates, regularity results for the transport equation associated with the geodesic flow and microlocal analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123975&date=2019-03-13Number Theory Seminar, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124585&date=2019-03-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124585&date=2019-03-13More Data, More Problems: What Society Needs from the Statistical and Data Sciences, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124481&date=2019-03-13
Despite more than 20 years of increasing reliance on data-intensive digital tools for commerce, governance, and social interaction, society has been slow to respond to both the promise and the perils of the phenomenon we now call Big Data. This lack of adaptation to new ways of collecting, storing, and analyzing data has been especially apparent within universities and the public sector, both of which have a responsibility to understand and regulate how innovative technologies make their way into the world.<br />
<br />
This talk outlines some of the biggest challenges for socially adapted data analysis, including biased data sources, proprietary data and analytical tools, antiquated regulatory frameworks in both academia and government, and an “engineering mindset” among developers and analysts that too often asks how to solve a problem but not why or whether to do so. I consider how university-based statistical and data scientific communities can promote an approach to data-driven research and teaching that is both rigorous and responsible.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124481&date=2019-03-13Chern Lectures, Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124304&date=2019-03-13
We will discuss questions about the relation between discrete phenomena and their continuous counterparts. This relates to extension of partially defined functions, Bourgain’s work on discretization and almost extension for a quantitative version of Ribe’s rigidity theorem, and differentiation questions that are well understood as infinitesimal phenomena but their macroscopic counterparts remain basic mysteries.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124304&date=2019-03-13Topology Seminar (Main Talk), Mar 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124522&date=2019-03-13
In the introductory talk, we discussed results on the evasion path problem for sensors wandering in a bounded domain in \(\mathbb R^n\). In the case of planar domains (\(n = 2\)), Adams and Carlsson provide a computable algorithm that determines the existence of an evasion path based on the time-varying alpha complex and the time-varying cyclic ordering on the set of sensors in the plane neighboring any given sensor. We provide a generalization of their result to \(\mathbb R^n\). Moreover, we show that their algorithm (and its generalization to \(\mathbb R^n\)) actually computes the number of connected components of the space of evasion paths and provides a representative path in each component.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124522&date=2019-03-13Applied Math Seminar, Mar 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123968&date=2019-03-14
In this presentation I will highlight the interplay between data science and computational science to efficiently solve real life large scale problems . The leading application that I will address is the numerical simulation of the heart function. The motivation behind this interest is that cardiovascular diseases unfortunately represent one of the leading causes of death in Western Countries. Mathematical models based on first principles allow the description of the blood motion in the human circulatory system, as well as the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart. This is a classical environment where multi-physics processes have to be addressed. Appropriate numerical strategies can be devised to allow an effective description of the fluid in large and medium size arteries, the analysis of physiological and pathological conditions, and the simulation, control and shape optimization of assisted devices or surgical prostheses. This presentation will address some of these issues and a few representative applications of clinical interest.<br />
<br />
Acknowledgment: The work presented in this talk is part of the project iHEART that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 740132)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123968&date=2019-03-14BIDS Data Science Lecture: The statistical mechanics of big data, Mar 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124343&date=2019-03-14
Constrained maximization of information entropy yields least biased probability distributions and provides a framework for construction of complex systems theory. From physics to economics, from forensics to medicine, this powerful inference method has enriched science. Here I explain this method, apply it to ecology, and show that it predicts the detailed shapes of numerous patterns in nature that are of interest to ecologists. In relatively undisturbed ecosystems the theory works remarkably well, but a systematic pattern of failure is observed for ecosystems either losing species following anthropogenic disturbance or diversifying in historical time. An approach to extending the theory to rapidly changing systems will be sketched.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124343&date=2019-03-14Chern Lecture/Mathematics Department Colloquium, Mar 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124305&date=2019-03-14
We will prove a sharp average-case variant of a classical embedding theorem of John through the theory of nonlinear spectral gaps. We will use this theorem to provide a new answer to questions of Johnson and Lindenstrauss (1983) and Bourgain (1985) on metric dimension reduction, and explain how it leads to unexpected algorithms for approximate nearest neighbor search.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124305&date=2019-03-14Gammage Seminar, Mar 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124651&date=2019-03-15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124651&date=2019-03-15'Information and Uncertainty in Data Science' Discussion Forum, Mar 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124353&date=2019-03-15
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
<br />
The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124353&date=2019-03-15Student Probability/PDE Seminar, Mar 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124540&date=2019-03-15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124540&date=2019-03-15Chern Lectures, Mar 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124306&date=2019-03-15
We will discuss coarse embeddings into Alexandrov spaces of nonpositive or nonnegative curvature. By studying subtle invariants that initially arose within the Ribe program and discretization questions, we will answer a question of Gromov (1993) about the coarse universality of Hadamard spaces. Connections to important questions such as the existence of super-expanders will be explained.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124306&date=2019-03-15Student Arithmetic Geometry Seminar, Mar 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124652&date=2019-03-15
We will prove the following statement: If $X$ is a smooth projective variety over a finite field $k$, and the Chow group of $0$-cycles is $\mathbb Z$, then $X$ has a rational point over $k$. We will start from the basic properties of rigid cohomology, then consider a decomposition theorem proved by Spencer Bloch, and finally give the proof by using the trace formula. In particular, the condition on $X$ is satisfied when $X$ is a Fano variety.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124652&date=2019-03-15Student 3-Manifold Seminar, Mar 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124653&date=2019-03-15
This is a continuation of the discussion about the existence and uniqueness of JSJ decompositions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124653&date=2019-03-15Combinatorics Seminar, Mar 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124520&date=2019-03-18
The Euler-Poincare formula is a cornerstone of the combinatorial theory of polytopes. It states that the number of faces of various dimensions of a convex polytope satisfy a linear relation and it is the only linear relation (up to scaling). Gram’s relation generalizes the fact that the sum of (interior) angles at the vertices of a convex $n$-gon is $(n-2)\pi$. In dimensions $3$ and up, it is necessary to consider angles at all faces. This gives rise to the interior angle vector of a convex polytope and Gram’s relation is the unique linear relation (up to scaling) among its entries. In this talk, we will consider generalizations of “angles” in the form of cone valuations. It turns out that the associated generalized angle vectors still satisfy Gram’s relation and that it is the only linear relation, independent of the notion of “angle”! To prove such a result, we rely on a very powerful connection to the combinatorics of zonotopes. The interior angle vector of a zonotope is independent of the chosen cone valuation and depends only on the associated lattice of flats. If time permits, we discuss flag-angles as a semi-discrete generalization of flag-vectors and their linear relations. This is joint work with Spencer Backman and Sebastian Manecke.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124520&date=2019-03-18Berkeley Statistics and Machine Learning Forum, Mar 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124349&date=2019-03-18
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
<br />
The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124349&date=2019-03-18String-Math Seminar, Mar 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124654&date=2019-03-18
I will describe joint work with Ciprian Manolescu on constructing an analogue of instanton Floer homology replacing the group \(SU(2)\) by \(SL(2,\mathbb C)\). Having failed to do so using the standard Floer theoretic tools of gauge theory and symplectic topology, we turned to sheaf theory to produce an invariant. After describing our approach, I will discuss some features of this theory that are expected to be visible from a Floer-theoretic point of view, but that we cannot currently access.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124654&date=2019-03-18Special Quantum Geometry Seminar, Mar 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124542&date=2019-03-18
Starting from the description of the Standard Model of particle physics based on noncommutative geometry we study the properties of the matrix algebras in the model. We demonstrate that there exists a new previously unknown geometric feature of the model, which can be mathematically stated that the Hilbert space of particles is a self-Morita equivalence bimodule for the associated generalization of the Clifford algebra. The experimental data support the existence of such property and, even more, some of the observed facts (like the neutrino and quark mass-mixing and the nondegeneracy of fermion masses) are necessary for it.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124542&date=2019-03-18Arithmetic Geometry and Number Theory RTG Seminar, Mar 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124608&date=2019-03-18
We discuss a new method to bound 5-torsion in class groups using elliptic curves. The most natural “trivial” bound on the n-torsion is to bound it by the size of the entire class group, for which one has a global class number formula. We explain how to make sense of the n-torsion of a class group intrinsically as a “dimension 0 selmer group”, and by embedding it into an appropriate Elliptic curve we can bound its size by the Tate-Shafarevich group which we can bound using the BSD conjecture. This fits into a general paradigm where one bounds “dimension 0 selmer groups” by embedding into global objects, and using class number formulas. (joint with Arul Shankar)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124608&date=2019-03-18Differential Geometry Seminar, Mar 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124648&date=2019-03-18
In contrast to finite time singularities of Ricci flows, it is known that collapsing with bounded sectional curvature may occur as we approach time infinity along immortal Ricci flows. In this talk I will show that along an immortal Ricci flow with uniformly bounded diameter and sectional curvature, an unbounded sequence of time slices sub converges to a Ricci flat orbifold.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124648&date=2019-03-18Seminar 217, Risk Management: Asset Insurance Premium in the Cross-Section of Asset Synchronicity, Mar 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122092&date=2019-03-19
Any asset can use some portfolio of similar assets to insure against its own factor risks, even if the identities of the factors are unknown. A long position of an asset and a short position of this portfolio forms an asset insurance premium (AIP) that is different from the equity risk premium. We estimate the AIP by projecting a stock’s return onto the entire asset returns span using a machine learning method. Stocks least (most) synchronized with other stocks earn a monthly AIP of 0.976% (0.305%). Asset synchronicity is countercyclical: high consumption growth correlates with low average asset insurance premium.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122092&date=2019-03-193-Manifold Seminar, Mar 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124673&date=2019-03-19
We will discuss a theorem of Bergeron-Haglund-Wise that hyperbolic arithmetic groups of simplest type are virtually special. This implies that geometrically finite subgroups are separable.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124673&date=2019-03-19Harmonic Analysis Seminar, Mar 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124722&date=2019-03-20
The $\varepsilon $–removal lemma of Tao converts a near-global family of bounds $\|Tf\|_{L^q(B(0,r)} \le O(r^\varepsilon \|f\|_{L^p})$ (as $r\to \infty $) to $\|Tf\|_{L^q(\mathbb R^d)} \le O( \|f\|_{L^{p+\delta }})$, for certain specific linear operators $T$. If the former holds for all positive $\varepsilon >0$ then one obtains a global bound with any exponent strictly $ >p$ on the right-hand side. This lemma is used to complete Guth's analysis of the Fourier “extension” operator. The proof and some applications of the result will be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124722&date=2019-03-20Topology Seminar (Introductory Talk), Mar 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122773&date=2019-03-20
I'll introduce three ways to build hyperbolic manifolds: arithmetic groups, "interbreeding", and "inbreeding". The first is purely algebraic. The second leads to the famous nonarithmetic examples of Gromov and Piatetski-Shapiro. The third is due to Agol, further studied by Belolipetsky-Thomson. Further, we will discuss concrete 3-dimensional examples via links in $S^3$ and belted sums.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122773&date=2019-03-20Metastability and Condensation, Mar 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124665&date=2019-03-20
Dynamical systems that are perturbed by small random noises are known to exhibit metastable behavior. Analogously, random walks with tendency towards a finite collection of sites may exhibit metastability.<br />
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Zero Range Process is a random walk on a simplex with metastable states residing at the vertices. Interpreting this process as a particle system on a one dimensional lattice, the metastable states correspond to the condensates. In this talk I give an overview of some known results in both the continuous and discrete settings, and discuss some open questions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124665&date=2019-03-20Number Theory Seminar, Mar 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124750&date=2019-03-20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124750&date=2019-03-20Topology Seminar (Main Talk), Mar 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122774&date=2019-03-20
I will explain why large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic hypersurfaces, answering a question of Reid and (independently) McMullen for $n=3$. These are the first examples of finite-volume $n$-hyperbolic manifolds, $n >2$, for which the collection of all finite-volume totally geodesic hypersurfaces is finite but nonempty. In this talk, I will focus mostly on dimension 3, where one can even construct link complements with this property. This is joint work with David Fisher, Jean-François Lafont, and Nicholas Miller.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122774&date=2019-03-20Facebook Disaster Maps: Aggregate Insights for Crisis Response and Recovery, Mar 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124492&date=2019-03-20
After a natural disaster or other crisis, humanitarian organizations need to know where affected people are located and what resources they need. While this information is difficult to capture quickly through conventional methods, aggregate usage patterns of social media apps like Facebook can help fill these information gaps. In this talk, I'll describe the data and methodology that power Facebook Disaster Maps. These maps utilize information about Facebook usage in areas impacted by natural hazards, producing aggregate pictures of how the population is affected by and responding to the hazard. The maps include insights into evacuations, cell site connectivity, access to electricity, and long-term displacement. In addition to descriptions and examples of each map type, I'll describe the source data used to generate the maps and efforts taken to ensure the security and privacy of Facebook users. I'll also describe limitations of our current methodologies and ongoing research aimed at improving our maps. I'll especially focus on our attempts to better measure long-term displacement after a crisis event.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124492&date=2019-03-20Paris/Berkeley/Bonn/Zürich Analysis Seminar, Mar 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124466&date=2019-03-21
The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in particular in regions where the water depth vanishes (the shoreline). The local well-posedness of the Green-Naghdi equations (and their justification as an asymptotic model for the water waves equations) has been extensively studied, but always under the assumption that the water depth is bounded from below by a positive constant. In this talk we will see how to remove this assumption. The problem then becomes a free-boundary problem since the position of the shoreline is unknown and driven by the solution itself. For the (hyperbolic) nonlinear shallow water equation, this problem is very related to the vacuum problem for a compressible gas. The Green-Naghdi equation include additional nonlinear, dispersive and topography terms with a complex degenerate structure at the boundary. In particular, the degeneracy of the topography terms makes the problem loose its quasilinear structure and become fully nonlinear. Dispersive smoothing also degenerates and its behavior at the boundary can be described by an ODE with regular singularity. These issues require the development of new tools, some of which of independent interest such as the study of the mixed initial boundary value problem for dispersive perturbations of characteristic hyperbolic systems, elliptic regularization with respect to conormal derivatives, or general Hardy-type inequalities. This is joint work with G. Métivier. Ref: D. Lannes and G. Métivier. The shoreline problem for the one-dimensional shallow water and Green- Naghdi equations. J. Ec. polytech. Math., 5:455–518, 2018.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124466&date=2019-03-21Applied Math Seminar, Mar 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124416&date=2019-03-21
Multi-scale kinetic equations can be compressed: in certain regimes, the Boltzmann equation is asymptotically equivalent to the Euler equations, and the radiative transfer equation is asymptotically equivalent to the diffusion equation. A lot of detailed information is lost when a system passes to the limit. In linear algebra, it is equivalent to a system being of low rank. I will discuss such transition and how it affects the computation: mainly, in the forward regime, inserting low-rankness could greatly advances the computation, while in the inverse regime, the system being of low rank typically makes the problems significantly harder.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124416&date=2019-03-21Gammage Seminar, Mar 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124851&date=2019-03-22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124851&date=2019-03-22'Information and Uncertainty in Data Science' Discussion Forum, Mar 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124736&date=2019-03-22
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
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The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124736&date=2019-03-22Student Probability/PDE Seminar, Mar 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124674&date=2019-03-22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124674&date=2019-03-22Logic Colloquium, Mar 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124609&date=2019-03-22
This talk is about joint work with Benjamin Steinberg, in which we apply model theory to study algebraic structures occurring in the theory of regular languages.<br />
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Regular languages can both be understood as monadic-second-order-definable classes of finite colored linear orders, and as subsets of the free monoid which induce a certain finite-index congruence, called the syntactic congruence. Definability in fragments of monadic second order logic then corresponds to the finite monoid quotient by the syntactic congruence having special properties. As the first and most famous instance of this correspondence theory, essentially due to Schützenberger, the class of languages definable in first-order logic coincides with the class of languages recognizable by an aperiodic (“subgroup-free”) monoid.<br />
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In this setting, questions about definability in logic thus lead to challenges that can often be resolved by studying finite monoids. Within this “finite algebra” approach to regular languages, free profinite objects are a useful tool, as they provide the appropriate notion of “equation”. In particular, the free pro-aperiodic monoid is a crucial algebraic object for studying the class of first-order definable languages.<br />
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The starting point of our work is the observation that Stone duality and Schützenberger’s Theorem together imply that elements of the free pro-aperiodic monoid may be viewed as elementary equivalence classes of pseudofinite words. Concretely, this means that one may 'compute' with elements of the free pro-aperiodic monoid as if they were finite words, in a way reminiscent of the methods of non-standard analysis. In particular, model theory provides us with saturated words in each class of pseudofinite words, i.e., words in which all possible factorizations are realized. We prove that such saturated words are stable under algebraic operations, and we give several applications of our new model-theoretic approach to pro-aperiodic monoids, including a solution to the word problem for $\omega$-terms that avoids using McCammond’s normal forms, as well as new proofs and extensions of other structural results concerning pro-aperiodic monoids.<br />
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Reference: S. J. v. Gool and B. Steinberg, Pro-aperiodic monoids via saturated models, Israel J. Math., accepted (2019). Preprint: https://arxiv.org/abs/1609.07736http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124609&date=2019-03-22Student Arithmetic Geometry Seminar, Mar 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124852&date=2019-03-22
I will discuss groupoid schemes and quotients in general and then state a result from a paper by Ekedahl that relates these quotients to Lie algebras for schemes over a field of positive characteristic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124852&date=2019-03-22Combinatorics Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124805&date=2019-04-01
Cluster algebras were introduced and studied in a series of articles by Fomin and Zelevinsky in [FZ02,FZ03,FZ07] and by Berenstein–Fomin–Zelevinsky in [BFZ05]. They admit connections to several branches of mathematics such as representation theory, geometry, and combinatorics. These algebras are defined by generators obtained recursively form an initial data (a quiver or a matrix). During this talk we will define cluster algebras and show examples. Provided the cluster algebra is acyclic (hence it is a Krull domain), we will show how to compute the associated class group just by looking at the initial data. As a result, we determine when a cluster algebra is a unique factorization domain. Eventually, such proofs rest entirely on tableau combinatorics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124805&date=2019-04-01Berkeley Statistics and Machine Learning Forum, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124350&date=2019-04-01
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
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The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124350&date=2019-04-01String-Math Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124650&date=2019-04-01
Based on the representation theory of quantum toroidal algebras we propose a generalization of the refined topological vertex formalism incorporating additional "Higgsed" vertices and lines apparently corresponding to refined Lagrangian branes. We find rich algebraic structure associated to brane diagrams incorporating the new vertices and lines. In particular, we build the screening charges associated to W-algebras of types \(gl(n)\) and \(gl(n|m)\), and more generally to Y-algebras of Gaiotto and Rapcak. The resulting refined partition functions coincide with partition functions of certain interacting 5d-3d-1d systems of quiver gauge theories (including quivers associated with superalgebras). Our formalism also automatically incorporates Ruijsenaars-Schneider Hamiltonians and their supersymmetric generalizations which act on the refined partition functions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124650&date=2019-04-01Northern California Symplectic Geometry Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125010&date=2019-04-01
After sketching the basics of derived algebraic geometry, I will explain how to define symplectic and lagrangian structures in this setting. A derived symplectic structure has a “shift” (or degree) that is zero for usual symplectic structures. This degree allows us a greater freedom, e.g. it leads to the fact that the derived intersection of two usual lagrangians is symplectic with a $-1$ shift. I will describe the basic existence theorems for symplectic structures on derived moduli spaces.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125010&date=2019-04-01Arithmetic Geometry and Number Theory RTG Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124367&date=2019-04-01
I will show a new, simple construction of crystals associated with toric hypersurfaces and exploit it to prove p-adic congruences for expansion coefficients of rational functions. This is joint work with Frits Beukers.<br />
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The exposition will be self-contained, but I shall explain that our ideas evolve from those of Bernard Dwork. Since he constructed an explicit Frobenius operator which does point counting for hypersurfaces, attempts to give a cohomological interpretaion of Dwork's work resulted in the Monsky–Washnitzer theory. Leaving out the $p$-adic counterpart, in 1990s Batyrev used solely the de Rham aspect of Dwork's theory to study mixed Hodge structure on the middle cohomology of toric hypersurfaces. Our construction basically adds the Frobenius structure back to this picture. As one of the applications, we will do a version of Katz's internal reconstruction of unit-root crystals via expansion coefficients of differential forms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124367&date=2019-04-01Differential Geometry Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124649&date=2019-04-01
We will give a brief review of the study of collapsed Riemannian manifolds with sectional curvature bounds, and we will report some recent progress on collapsed manifolds with Ricci curvature and local rewinding volume bounded below.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124649&date=2019-04-01Northern California Symplectic Geometry Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125011&date=2019-04-01
In previous work, Hutchings, Ramos and I studied the embedded contact homology (ECH) spectrum for any closed three-manifold with a contact form, and proved a “volume identity” showing that the leading order asymptotics recover the contact volume. I will explain recent joint work that sharpens this asymptotic formula by estimating the subleading term. The main technical point needed in our work is an improvement of a key spectral flow bound in Taubes' proof of the three-dimensional Weinstein conjecture; the main goal of my talk will be to explain the ideas that go into this improvement. I will also discuss some possibilities for obtaining sharp asymptotics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125011&date=2019-04-01Analysis and PDE Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124368&date=2019-04-01
Carleson proposed a problem on a.e. convergence for free Schrödinger solutions as time goes to zero. Recently it got a sharp answer (up to the endpoint) in all dimensions. We will talk about the new result in dimensions $n+1$ for all $n >2$ and ideas behind it (joint work with Xiumin Du).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124368&date=2019-04-01Seminar 217, Risk Management: Robust Experimentation in the Continuous Time Bandit Problem, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122093&date=2019-04-02
We consider the experimentation dynamics of a decision maker (DM) in a two-armed bandit setup, where the agent holds ambiguous beliefs regarding the distribution of the return process of one arm and is certain about the other one. The DM entertains Multiplier preferences a la Hansen and Sargent [2001], thus we frame the decision making environment as a two-player differential game against nature in continuous time. We characterize the DM's value function and her optimal experimentation strategy that turns out to follow a cut-off rule with respect to her belief process. The belief threshold for exploring the ambiguous arm is found in closed form and is shown to be increasing with respect to the ambiguity aversion index. We then study the effect of provision of an unambiguous information source about the ambiguous arm. Interestingly, we show that the exploration threshold rises unambiguously as a result of this new information source, thereby leading to more conservatism. This analysis also sheds light on the efficient time to reach for an expert opinion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122093&date=2019-04-02Student Harmonic Analysis and PDE Seminar (HADES), Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124369&date=2019-04-02
The Fourier extension operator is a very interesting and difficult object to study in harmonic analysis. Stein conjectured that it is a bounded linear operator between some $L^p$ spaces. Recently people have found that auxiliary real polynomials can help one study Stein's above Restriction Conjecture. We will talk about a few interesting facts about zero sets of real polynomials, and why they can be useful in the study of the Restriction Conjecture.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124369&date=2019-04-023-Manifold Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125016&date=2019-04-02
We'll describe subgroup separability for arithmetic hyperbolic manifolds of simplest type and apply it to describe embedding results due to Kolpakov-Reid-Slavich. With this we can address a conjecture of Claude LeBrun that the Seiberg-Witten invariants of hyperbolic 4-manifolds vanish, by showing the existence of examples for which it is true. Joint with Francesco Lin.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125016&date=2019-04-02Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124984&date=2019-04-02
An artinian local ring $(R,m)$ is called Gorenstein if it has a unique minimal ideal. If $R$ is graded, then it is called Koszul if $R/m$ has a linear $R$-free resolution. Any Koszul algebra is defined by quadratic relations, but the converse is false, and no one knows a finitely computable criterion. Both types of rings occur in many situations in algebraic geometry and commutative algebra, and in many cases, a Gorenstein quadratic algebra coming from geometry is often Koszul (e.g. homogeneous coordinate rings of most canonical curves).<br />
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In 2001, Conca, Rossi, and Valla asked the question: must a (graded) quadratic Gorenstein algebra of regularity 3 be Koszul?<br />
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I will talk about techniques for deciding whether a quadratic Gorenstein algebra is Koszul and methods for generating many examples which are not Koszul. We will explain how these methods provide a negative answer to the above question, as well as a complete picture in the case of regularity at least 4. (This is joint work with Hal Schenck and Matt Mastroeni).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124984&date=2019-04-02Tajima coalescent, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124950&date=2019-04-02
In this talk I will present the Tajima coalescent, a model on the ancestral relationships of molecular samples. This model is then used as a prior model on unlabeled genealogies to infer evolutionary parameters with a Bayesian nonparametric method. I will then show that conditionally on observed data and a particular mutation model, the cardinality of the hidden state space of Tajima’s genealogies is exponentially smaller than the cardinality of the hidden state space of Kingman’s genealogies. We estimate the corresponding cardinalities with sequential importance sampling. Finally, I will propose a new distance on unlabeled genealogies that allows us to compare different distributions on unlabeled genealogies to Tajima’s coalescent.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124950&date=2019-04-02Representation Theory and Mathematical Physics Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125008&date=2019-04-02
We present a solution of the matrix Bochner problem, a long-standing open problem in the theory of orthogonal polynomials, with applications to diverse areas of research including representation theory, random matrices, spectral theory, and integrable systems. Our solution is based on ideas applied by Krichever, Mumford, Wilson and others, wherein the algebraic structure of an algebra of differential operators influences the values of the operators within the algebra. By using a similar idea, we convert the matrix Bochner problem to one about noncommutative algebras of GK dimension 1 which are module finite over their centers. Then the problem is resolved using the representation theory of these algebras.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125008&date=2019-04-02CANCELED: Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124985&date=2019-04-02
I will tell the story of equivariant completion of toric varieties and their degenerations from the perspectives of algebraic geometry and combinatorics. We will start on the algebraic geometry side with results of Nagata and Sumihiro on completions of varieties. We will then move on to later combinatorial proofs that normal toric varieties admit completions. Finally, we will discuss recent results which show that certain degenerations of toric varieties admit equivariant completions. We will see that, in contrast to the earlier part of the story, the algebraic-geometric proof does not show the existence of normal equivariant completions, whereas the combinatorial proof does.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124985&date=2019-04-02Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124992&date=2019-04-02
After reviewing classical results about existence of completions of varieties, I will talk about a class of degenerations of toric varieties which have a combinatorial classification - normal toric varieties over rank one valuation rings. I will then discuss recent results about the existence of equivariant completions of such degenerations. In particular, I will show a new result about the existence of normal equivariant completions of these degenerations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124992&date=2019-04-02Topology Seminar (Introductory Talk), Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124990&date=2019-04-03
Part of the Deligne–Mumford compactification of the moduli space of marked Riemann surfaces comes from the collision of marked points ("bubbling"). I will explain this kind of degeneration and then talk about a real analogue of such compactification in the study of constant curvature conical metrics, where a similar bubbling behavior appears.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124990&date=2019-04-03Deformation Theory Seminar, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125064&date=2019-04-03
We will review Orlov’s construction of an equivalence of categories between certain Calabi-You complete intersection in weighted protective spaces and the equivariant matrix factorization of associated quasihomogeneois singularitieshttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125064&date=2019-04-03Grace-like polynomials and related questions, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124979&date=2019-04-03
We say that the multi-affine polynomial P(z1, . . . , zm, w1, . . . , wn) is Grace-like if it does not vanish when {z1, . . . , zm is separated from {w1, . . . , wn) by a circle in the complex plane. Such polynomials have many unexpected probabilistic properties related to the work of Borcea-Brändén.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124979&date=2019-04-03Number Theory Seminar, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125015&date=2019-04-03
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125015&date=2019-04-03Topology Seminar (Main Talk), Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124991&date=2019-04-03
The problem of finding and classifying constant curvature metrics with conical singularities has a long history bringing together several different areas of mathematics. This talk will focus on the particularly difficult spherical case where many new phenomena appear. When some of the cone angles are bigger than $2\pi $, uniqueness fails and existence is not guaranteed; smooth deformation is not always possible and the moduli space is expected to have singular strata. I will give a survey of several recent results regarding this singular uniformization problem, connecting PDE techniques with complex analysis and synthetic geometry. Based on joint works with Rafe Mazzeo and Bin Xu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124991&date=2019-04-03Applied Math Seminar, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124539&date=2019-04-04
Adversarial path planning problems are important in robotics applications and in modeling the behavior of humans in dangerous environments. Surveillance-Evasion (SE) games form an important subset of such problems and require a blend of numerical techniques from multiobjective dynamic programming, game theory, numerics for Hamilton-Jacobi PDEs, and convex optimization. We model the basic SE problem as a semi-infinite zero-sum game between two players: an Observer (O) and an Evader (E) traveling through a domain with occluding obstacles. O chooses a pdf over a finite set of predefined surveillance plans, while E chooses a pdf over an infinite set of trajectories that bring it to a target location. The focus of this game is on "E's expected cumulative exposure to O", and we have recently developed an algorithm for finding the Nash Equilibrium open-loop policies for both players. I will use numerical experiments to illustrate algorithmic extensions to handle multiple Evaders, moving Observes, and anisotropic observation sensors. Time permitting, I will also show preliminary results for a very large number of selfish/independent Evaders modeled via Mean Field Games.<br />
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Joint work with M.Gilles, E.Cartee, and REU-2018 participants.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124539&date=2019-04-04Statistical and Computational Challenges in Conformational Biology, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125018&date=2019-04-04
Chromatin architecture is critical to numerous cellular processes including gene regulation, while conformational disruption can be oncogenic. Accordingly, discerning chromatin configuration is of basic importance, however, this task is complicated by a number of factors including scale, compaction, dynamics, and inter-cellular variation.<br />
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The recent emergence of a suite of proximity ligation-based assays, notably Hi-C, has transformed conformational biology with, for example, the elicitation of topological and contact domains providing a high resolution view of genome organization. Such conformation capture assays provide proxies for pairwise distances between genomic loci which can be used to infer 3D coordinates, although much downstream analysis bypasses this reconstruction step.<br />
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After demonstrating advantages deriving from obtaining 3D genome reconstructions, in particular from superposing genomic attributes on a reconstruction and identifying extrema (â€™3D hotspotsâ€™) thereof, we showcase methodological challenges surrounding such analyses, as well as advancing a novel reconstruction approach based on principal curves. Open issues highlighted include (i) performing and synthesizing reconstructions from single-cell assays, (ii) devising rotation invariant methods for 3D hotspot detection, (iii) assessing genome reconstruction accuracy, and (iv) averting reconstruction uncertainty by direct integration of Hi-C data and genomic features. By using p-values from (epi)genome wide association studies as the feature the latter approach provides a conformational lens for viewing GWAS findings.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125018&date=2019-04-04'Information and Uncertainty in Data Science' Discussion Forum, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124354&date=2019-04-05
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
<br />
The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124354&date=2019-04-05Student Probability/PDE Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125014&date=2019-04-05
For $\alpha >0$, the $\alpha$-Lipschitz minorant of a càdlàg function f is the greatest $\alpha$-Lipschitz function that is dominated by f. We study the joint law of any two-sided Lévy process $(X_t)_{t \in \mathbb R}$ and its $\alpha$-Lipschitz minorant $(M_t)_{t \in \mathbb R}$. In particular, we consider $\mathcal Z$ to be the set of points where $X$ meets $M$, and prove that $((X_t),\mathcal Z)$ is a stationary and regenerative space-time system. Under some determined conditions, when the set $\mathcal Z$ is almost surely discrete, we have an i.i.d sequence of excursions of X above M. In the special case, when X is a Brownian motion with drift, we give explicit path decompositions of those excursions. This $\alpha$-Lipschitz minorant appears as the solutions of the Hamilton-Jacobi PDE when the initial condition is a Lévy noise and the corresponding Lagrangian is of the form $L(v)=\alpha \vert v \vert$. This talk is based on a joint work with Steven N. Evans.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125014&date=2019-04-05Special Quantum Geometry Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125069&date=2019-04-05
Assuming that both temperature and pressure are continuous functions, we can conclude that there are always two antipodal points on Earth with exactly the same pressure and temperature. This is the two-dimensional version of the celebrated Borsuk-Ulam Theorem which states that for any continuous map from the n-dimensional sphere to n-dimensional real Euclidean space there is always a pair of antipodal points on the sphere that are identified by the map. Our quest to unravel topological mysteries in the Middle Earth of quantum spaces will begin with gentle preparations in the Shire of elementary topology. Then, after riding swiftly through the Rohan of C*-algebras and Gelfand-Naimark Theorems, and carefully avoiding the Mordor of incomprehensible technicalities, we shall arrive in the Gondor of compact quantum groups acting freely on unital C*-algebras. It is therein that the noncommutative Borsuk-Ulam-type conjecture dwells waiting to be proven or disproven. After revealing how to prove the conjecture assuming some torsion or local-triviality properties, we shall explain how the general case (no torsion or local-triviality assumptions) implies the famous and long-standing weak Hilbert-Smith conjecture. To end with, we will explain how a certain special case of the conjecture can be interpreted as the non-contractibility of non-trivial compact quantum groups, and prove it for some classes of compact quantum groups. (Based on joint works with Paul F. Baum, Ludwik Dabrowski, Eusebio Gardella, Sergey Neshveyev, Mariusz Tobolski and Jianchao Wu.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125069&date=2019-04-05Deformation Theory Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125065&date=2019-04-05
We will discuss the appearance of superpotentials for matrix factorizations from the symplectic side of Mirror Symmetry in the SYZ construction, with the monomial terms corresponding to components of the canonical boundary divisor.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125065&date=2019-04-05Logic Colloquium, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124610&date=2019-04-05
I will present some recent applications of Model Theory to uniform bounds in questions arising from Number Theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124610&date=2019-04-05Student 3-Manifold Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125122&date=2019-04-05
Compact surfaces with non-positive Euler characteristic can be inductively decomposed by cutting along finitely many properly embedded loops and arcs until one is left with a collection of disks; such a decomposition is called a hierarchy. An analogue up a dimension is called a Haken manifold, which can be inductively decomposed by cutting along two-sided incompressible surfaces until one is left with a collection of balls. Examples of Haken manifolds include link complements and surface bundles over circles. Certain facts about Haken manifolds can be proved by induction on a hierarchy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125122&date=2019-04-05Probabilistic Operator Algebra Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124538&date=2019-04-08
Chordal Loewner equations have been shown to be connected with evolution equations for semigroups in monotone probability. I will briefly recall these connections and then discuss recent related work of Franz, Hasebe and Schleissinger which uses these connections to probability measures on $\mathbb R$ with univalent Cauchy transform and some of the analytic and geometric properties thereof. Time permitting, I will also discuss results in the multiplicative setting.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124538&date=2019-04-08Combinatorics Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124983&date=2019-04-08
We provide an insertion algorithm from generalized permutations (or two-line arrays subject to certain conditions) and pairs of standard Young tableaux and multiset tableaux of the same shape. If we insert the propagating blocks of partition diagrams we get natural sets of tableaux and the number of these tableaux of a fixed shape are equal to the dimensions of irreducible representations indexed by the same shape. This is joint work with Laura Colmenarejo, Rosa Orellana, Franco Saliola and Mike Zabrocki.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124983&date=2019-04-08Arithmetic Geometry and Number Theory RTG Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125099&date=2019-04-08
The Birch and Swinnerton-Dyer conjecture is known in the case of rank 0 and 1 thanks to the foundational work of Kolyvagin and Gross-Zagier. In this talk, I will report on a joint work in progress with Yifeng Liu, Yichao Tian, Wei Zhang, and Xinwen Zhu. We study the analogue and generalizations of Kolyvagin's result to the unitary Gan-Gross-Prasad paradigm. More precisely, our ultimate goal is to show that, under some technical conditions, if the central value of the Rankin-Selberg L-function of an automorphic representation of U(n)*U(n+1) is nonzero, then the associated Selmer group is trivial; Analogously, if the Selmer class of certain cycle for the U(n)*U(n+1)-Shimura variety is nontrivial, then the dimension of the corresponding Selmer group is one.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125099&date=2019-04-08Differential Geometry Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125009&date=2019-04-08
Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the interior of the Kähler cone must have a convergent subsequence. As an application, we prove the existence of global moduli spaces of scalar-flat Kähler ALE metrics for several infinite families of Kähler ALE spaces. Joint with J. Viaclovskyhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125009&date=2019-04-08David Morton — Models and Algorithms for Multi-stage Stochastic Programming, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125022&date=2019-04-08
Abstract: We consider two classes of multi-stage stochastic linear programs (MSLPs) that lend themselves to solution by stochastic dual dynamic programming (SDDP). First, we consider a distributionally robust MSLP. Here, the specific realizations in each stage are fixed, and distributional robustness is with respect to the probability mass function governing those realizations. Second, we consider a class of partially observable MSLPs. In both cases, we describe a computationally tractable variant of SDDP to solve the model. This is joint work with Oscar Dowson, Daniel Duque, and Bernardo Pagnoncelli.Bio: David Morton is the David A. and Karen Richards Sachs Professor and Department Chair of Industrial Engineering & Management Sciences at Northwestern University. He received his PhD in Operations Research from Stanford University. He was a Fulbright Research Scholar at Charles University in Prague, a National Research Council Postdoctoral Fellow in the Operations Research Department at the Naval Postgraduate School, and is an INFORMS Fellow.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125022&date=2019-04-08Analysis and PDE Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123670&date=2019-04-08
I will explain how the results of Bourgain, Burq and the speaker '13 can be used to obtain control and observability by rough functions and sets on 2-tori. We show that for the time dependent Schrödinger equation, any set of positive measure can be used for observability and controllability. For non-empty open sets this follows from the results of Haraux '89 and Jaffard '90, while for sufficiently long times and rational tori this can be deduced from the results of Jakobson '97. Other than tori (of any dimension; cf. Komornik '91, Anantharaman–Macia '14) the only compact manifolds for which observability holds for any non-empty open sets are hyperbolic surfaces. That follows from results of Bourgain–Dyatlov '16 and Dyatlov–Jin '17 and I will discuss the difficulty of passing to rougher rougher sets in that case. Joint work with N Burq.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123670&date=2019-04-08CANCELED: Seminar 217, Risk Management: No Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122094&date=2019-04-09
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122094&date=2019-04-09Student Harmonic Analysis and PDE Seminar (HADES), Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125007&date=2019-04-09
I will present a microlocal approach to some of the analytical problems in hyperbolic dynamics. Applications include exponential decay of correlations and a definition of Pollicott-Ruelle resonances for hyperbolic systems. The intuition comes from scattering theory, with scattering happening as frequency goes to infinity. Based on joint work with Maciej Zworski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125007&date=2019-04-093-Manifold Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125141&date=2019-04-09
We’ll introduce some preliminaries such as Hodge theory and spin structure for Seiberg-Witten invariants on 4-manifolds. Then a nice nonlinear PDE on the spin bundle of 4-manifolds will give rise to a moduli space related to Seiberg-Witten invariants. We will also discuss some related results of hyperbolic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125141&date=2019-04-09Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125117&date=2019-04-09
One consequence of the recent push to develop a scheme theory in tropical geometry has been the development of a tropical commutative algebra. This starts with the commutative algebra of semirings, but in order to get a theory that interacts with geometry, we are lead to impose some combinatorial, matroid-theoretic, conditions. I will introduce these ideas, and discuss the current state of our understanding.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125117&date=2019-04-09Representation Theory and Mathematical Physics Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125135&date=2019-04-09
Spherical varieties are algebraic varieties with an action by a reductive group which admit an open Borel orbit. This extra condition on its symmetries connects their study to representation theory, makes tractable their classification, and yet is broad enough to have many rich examples.<br />
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We introduce a definition of a spherical supervariety, which is a simple generalization of the classical definition to the super world. Then, with a focus on the affine case, we look at certain properties of these spaces, highlighting some of the differences and similarities with the classical story.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125135&date=2019-04-09Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125136&date=2019-04-09
Last week Mike Stillman spoke about recent investigations of Koszul algebras. I'll give some more general background on resolutions of the residue field of a local ring, and talk about work of Conca and others on bounds for the syzygies of a Koszul ring.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125136&date=2019-04-09Harmonic Analysis Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125182&date=2019-04-10
The title refers to inequalities of the form $\int _{[0,1]^d} \prod _{j=1}^d f_j(x_j) \,e^{i\lambda \psi (x)}\,dx = O(|\lambda |^{-\gamma } \prod _j \|f_j\|_{L^{p_j}})$ for large $\lambda \in {\mathbb R}$. Here $\psi :{\mathbb R}^d\to {\mathbb R}$ is a smooth phase function, and the exponent γ depends on ψ and on the exponents $p_j$. These inequalities are well understood in the bilinear case $d=2$, and sharp bounds have been obtained by Phong-Stein-Sturm and Gilula-Gressman-Xiao for certain parameter ranges for $d >2$. Nonetheless, the case $d\ge 3$ remains largely mysterious. I will argue that the most basic question in this context remains unaddressed for $d\ge 3$, and will present recent partial results and examples for $d=3$ with an outline of the proofs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125182&date=2019-04-10Topology Seminar (Introductory Talk), Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125012&date=2019-04-10
Given a pseudo-Anosov mapping class of a closed orientable surface, there exists a finite cover of the surface to which the mapping class lifts, such that the induced action on the first homology has at least one eigenvalue lying outside of the unit circle. In this talk, I will review some background related to the above result, and its relations with twisted Reidemeister torsion and Fried's cone of homological directions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125012&date=2019-04-10Deformation Theory Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125181&date=2019-04-10
We will review the theory of curved deformations, based largely on a recent paper by Blanc-Katzarkov-Pandit and earlier work of Preygel. (Mind that the Hill shuttle is not running this Wednesday!)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125181&date=2019-04-10Bigeodesics in first and last passage percolation, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125095&date=2019-04-10
First and last passage percolation are statistical physics models of<br />
random growth. These models are widely believed to belong to the<br />
Kardar-Parisi-Zhang universality class. I will define these two models<br />
and talk about what it means to be in this universality class. A<br />
longstanding question about these models is whether they have<br />
bi-infinite geodesics. This question is of interest to physicists due<br />
to its connections to the Ising model. I will discuss the recent<br />
progress on this question. This talk is based on joint work with<br />
Daniel Ahlberg, Riddhipratim Basu and Allan Sly.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125095&date=2019-04-10BIDS Data Science Lecture: Do as eye do: efficient content-adaptive processing and storage of large fluorescence images, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124344&date=2019-04-10
Modern microscopes create a data deluge with gigabytes of data generated each second, and terabytes per day. Storing and processing this data is a severe bottleneck, not fully alleviated by data compression. We argue that this is because images are processed as grids of pixels. To address this, we developed a content-adaptive representation of fluorescence microscopy images, the Adaptive Particle Representation (APR). The APR replaces pixels with particles positioned according to image content. The APR not only overcomes storage bottlenecks, as data compression does, but additionally overcomes memory and processing bottlenecks since the adaptivity can be used during processing tasks. In this talk, I will introduce the ideas and concepts of the APR, its performance on experimental data, and show how the APR can be used to enhance, rather than replace, existing algorithms and approaches, including applications to machine learning. Beyond image-processing I will also present how the APR can be used for adaptive resolution simulations, and discuss work on robust methods for data-driven model discovery for spatial-temporal data.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124344&date=2019-04-10Number Theory Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125100&date=2019-04-10
The Farey fractions of level $n$ are the set of rationals in $[0,1]$ in lowest terms having denominator at most $n$. It is known that a measure of equally weighted point masses (of total mass 1) on the points of the Farey sequence $F_n$ converges to the uniform distribution on $[0,1]$ as $n$ goes to infinity. The Riemann hypothesis is equivalent to suitably fast rates of convergence (to zero) of certain statistics measuring distance to uniform distribution, given by theorems of Franel (1924) and Landau (1924) . This talk addresses a toy model consisting of unreduced Farey fractions (allowing fractions not in lowest terms) and studies similar statistics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125100&date=2019-04-10Renewable Estimation and Incremental Inference in Generalized Linear Models with Streaming Data, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124960&date=2019-04-10
I will present a new statistical paradigm for the analysis of streaming data based on renewable estimation and incremental inference in the context of generalized linear models. Our proposed renewable estimation enables us to sequentially update the maximum likelihood estimation and inference with current data and summary statistics of historic data, but with no use of any historic raw data themselves. In the implementation, we design a new data flow, called the Rho architecture to accommodate the data storage of current and historic data, as well as to communicate with the computing layer of the Spark system in order to facilitate sequential learning. We establish both estimation consistency and asymptotic normality for the renewable estimation and incremental inference for regression parameters. We illustrate our methods by numerical examples from both simulation experiments and real-world analysis. This is a joint work with Lan Luo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124960&date=2019-04-10Representation Theory and Mathematical Physics Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124993&date=2019-04-10
The problem of constructing global action-angle variables on coadjoint orbits of compact Lie groups is one of the interesting questions in the theory of integrable systems. A fundamental contribution was made by Guillemin-Sternberg who constructed the Gelfand-Zeitlin integrable systems on coadjoint orbits of the groups \(SU(n)\) and \(SO(n)\). Recently, toric degeneration techniques allowed for the construction of global action-angle variables on rational coadjoint orbits of compact Lie groups of all types.<br />
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In this talk, I will present a new approach which aims at constructing global action-angle coordinates on all regular coadjoint orbits of compact Lie groups and on a large family of related Hamiltonian spaces. It combines the results of Ginzburg-Weinstein on the theory of Poisson-Lie groups and the theory of cluster algebras using the "partial tropicalization” procedure.<br />
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The talk is based on joint works with A. Alekseev, A. Berenstein, B. Hoffman, and J. Lane.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124993&date=2019-04-10Topology Seminar (Main Talk), Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125013&date=2019-04-10
Given a mapping class of a closed orientable surface, we look at any lift of the mapping class to any finite cover of the surface. An eigenvalue of the induced homological action of the lift will be called a virtual homological eigenvalue. How much about the mapping class can we learn through virtual homological eigenvalues? In this talk, I will discuss some results related to this question. In particular, I will present some ways to combine the Nielsen fixed point theory with the more recent virtual specialization techniques in 3-manifold topology.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125013&date=2019-04-10Mathematics Department Colloquium, Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124948&date=2019-04-11
A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions.There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff type surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems. Joint works with A. Ghosh and with J. Bourgain and A. Gamburd.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124948&date=2019-04-11Bay Area Microlocal Analysis Seminar, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124751&date=2019-04-12
Consider the semiclassical Schrödinger equation $(h^2\Delta +V-E)u=0$, where, instead of being smooth, $V$ is allowed to be singular across a hypersurface. The singularity in the potential turns out to have very interesting consequences for the structure of solutions $u$; in effect, WKB solutions include not just contributions from classical propagation across the interface but also reflected singularities, in what amounts to a quantum diffraction effect (meaning one that is not visible at the level of classical Hamiltonian dynamics). I will discuss the propagation and reflection of semiclassical singularities in this setting, and also its consequences for the existence of quantum resonances in systems where trajectories escape to infinity under classical flow but not under the branched flow where we allow reflections. This is joint work with Oran Gannot.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124751&date=2019-04-12Student Probability/PDE Seminar, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125179&date=2019-04-12
We present the work of Armstrong, Cardaliaguet, and Souganidis, who prove convergence rates for stochastic homogenization using a mixture of probability techniques and PDE techniques. We discuss the metric problem, its rate of convergence, its relation to approximate correctors, and the reduction of the full problem to that of approximate correctors.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125179&date=2019-04-12Bay Area Microlocal Analysis Seminar, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124809&date=2019-04-12
We discuss the recent developments in the inverse length spectral theory of smooth strictly convex domains, including the works of Avila–De Simoi–Kaloshin and Kaloshin–Sorrentino on the Birkhoff conjecture, and De Simoi–Kaloshin–Wei on the length spectral rigidity of nearly circular domains with a reflectional symmetry. In a joint work with Zelditch we explore the inverse Laplace spectral problem for nearly circular ellipses, among all smooth domains without any symmetry or convexity assumption.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124809&date=2019-04-12Combinatorics Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125178&date=2019-04-15
The classical Dehn–Sommerville equations, relating the face numbers of simplicial polytopes, have an analogue for cubical polytopes. These relations can be generalized to apply to simplicial and cubical Eulerian complexes. In this talk, we will introduce a few different known proofs of the classical Dehn–Sommerville relations for simplicial complexes, relating this result to concepts such as zeta polynomials of posets, Ehrhart polynomials of simplicial complexes, and chain-partitions of posets. We will then discuss whether each proof idea can be adapted to the cubical case.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125178&date=2019-04-15Berkeley Statistics and Machine Learning Forum, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124351&date=2019-04-15
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
<br />
The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124351&date=2019-04-15Probabilistic Operator Algebra Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123139&date=2019-04-15
A landmark result of Dykema in 1993 classified free products of tracial finite dimensional von Neumann algebras in terms of interpolated free group factors. In 1997, Shlyakhtenko constructed the free Araki-Woods factors, a natural type III analogue of the free group factors. He asked whether arbitrary free products of non-tracial finite-dimensional von Neumann algebras can always be expressed in terms of free Araki-Woods factors. Partial progress on this problem was obtained by Houdayer and Ueda. In this talk we will answer Shlyakhtenko's question in the affirmative. The key tool we use is a non-tracial free graph von Neumann algebra which will be used to realize some of these free products. This is joint work with Brent Nelson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123139&date=2019-04-15Arithmetic Geometry and Number Theory RTG Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125211&date=2019-04-15
Classical Serre-Tate theory concerns the deformation theory of ordinary abelian varieties. It implies that their deformation spaces can be equipped with a group structure and a lifting of the Frobenius morphism, and consequently such varieties admit a canonical lifting to characteristic zero. In the first half of the talk, aimed at graduate students and people with no prior exposure to the topic, I will review the classical results in this direction.<br />
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In the second half, I will show how to obtain similar results for ordinary Calabi-Yau varieties of arbitrary dimension. The main tools will be Frobenius splittings and Witt vectors of length two. This is joint work with Maciej Zdanowicz (EPFL).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125211&date=2019-04-15Differential Geometry Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125046&date=2019-04-15
We discuss the development on geometric and analytic aspects of the Anomaly flow. Such flow naturally arises in the study of a system of equations for supersymmetric vacua of superstrings proposed independently by C. Hull and A. Strominger in 1980s. The system allows non-vanishing torsion and they incorporate terms which are quadratic in the curvature tensor. As such they are also particularly interesting from the point of view of both non-Kaehler geometry and the theory of nonlinear partial differential equations. It turns out that the corresponding flow shares some features with the Ricci flow and preserves the conformally balanced condition of Hermitian metrics. This talk is based on joint works with D. Phong and S. Picard.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125046&date=2019-04-15Analysis and PDE Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125198&date=2019-04-15
In this talk we discuss the problem of global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Several physical models related to general relativity have shown the importance of studying such systems but very few results are known at present in low space dimension, where linear solutions slowly decay in time.<br />
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We study here a model quadratic quasilinear two-dimensional system, in which the nonlinearity writes in terms of “null forms”, and prove global existence by propagating a-priori energy estimates and optimal uniform estimates on the solution. In proving such estimates one has to deal with several issues such as the quasilinear nature of the problem, the very low decay in time of quadratic nonlinearities, the fact that initial data are not compactly supported…<br />
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We will show how to obtain energy estimates by using systematically quasilinear normal forms, in their para-differential version. Uniform estimates will instead be recovered by deducing a new coupled system of a transport equation and an ordinary differential equation from the starting PDE system by means of a semiclassical microlocal analysis of the problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125198&date=2019-04-15Seminar 217, Risk Management: Linking 10-K and the GICS - through Experiments of Text Classification and Clustering, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122096&date=2019-04-16
A 10-K is an annual report filed by a publicly traded company about its financial performance and is required by the U.S. Securities and Exchange Commission (SEC). 10-Ks are fairly long and tend to be complicated. But this is one of the most comprehensive and most important documents a public company can publish on a yearly basis. The Global Industry Classification Standard (GICS) is an industry taxonomy developed in 1999 by MSCI and S&P Dow Jones Indices and is designed to classify a company according to its principal business activity. The GICS hierarchy begins with 11 sectors and is followed by 24 industry groups, 68 industries, and 157 sub-industries. We ask two questions: First, can a classifier be trained to recognize a firm's GICS sector based on the textual information in its 10-K? Second, can we extract, from the classifier, embeddings (low dimensional vectors) for 10-Ks that respect their GICS sectors, so firms within the same sector would have embeddings that are close (measured by cosine similarity)? We report on a series of experiments with Convolutional Neural Network (CNN) for text classification, trained on two variants of document representations, one uses pre-trained word vectors, the other is based on the simple bag-of-words model.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122096&date=2019-04-16Probabilistic Operator Algebra Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125197&date=2019-04-16
A homogeneous noncommutative degree $d$ polynomial $p$ has a $t$-term real Waring (resp. complex Waring) decomposition provided that $p(x)$ can be written as the sum of $t$ terms of the $d^{th}$-power of linear functions of $x$, i.e. \[ p(x)=\sum _{s=1}^t [ A^s_1x_1 + A^s_2x_2 + ... A^s_gx_g]^d \] with real (resp. complex) numbers $A_j^s$. The talk will analyze this, some consequences and extensions.<br />
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If time permits there will be a sketch of some other recent results drawn from free analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125197&date=2019-04-16Student Harmonic Analysis and PDE Seminar (HADES), Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125272&date=2019-04-16
In this talk we will discuss bases in Banach lattices, and how they can be used to measure (non)-embeddability of a Banach space into a lattice. We will give several characterizations of basic sequences that "respect the lattice structure", and discuss some of the more unexpected corollaries. Time permitting, I will comment on existence of non-negative bases in Hilbert space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125272&date=2019-04-16Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125267&date=2019-04-16
Let $R$ be a standard graded algebra over a field. We investigate how the singularities of $\operatorname {Spec} R$ or $\operatorname {Proj} R$ affect the $h$-vector of $R$, which is the coefficients of the numerator of its Hilbert series. The most concrete consequence of our work asserts that if $R$ satisfies Serre's condition $(S_r)$ and have reasonable singularities (Du Bois on the punctured spectrum or $F$-pure), then $h_0,\dots , h_r\geq 0$. Furthermore the multiplicity of $R$ is at least $h_0+h_1+\dots +h_{r-1}$. We also prove that equality in many cases forces $R$ to be Cohen-Macaulay. This is joint work with Linquan Ma and Matteo Varbaro.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125267&date=2019-04-16Representation Theory and Mathematical Physics Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125067&date=2019-04-16
I will talk about the underlying homotopical structures within field equations, which emerge in string theory as conformal invariance conditions for sigma models. I will show how these, often hidden, structures emerge from the homotopy Gerstenhaber algebra associated to vertex and Courant algebroids, thus making all such equations the natural objects within vertex algebra theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125067&date=2019-04-16Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125268&date=2019-04-16
The Hilbert scheme of n points in $P^2$ is smooth of dimension 2n and the tangent space to any (monomial) ideal admits a nice combinatorial description. On the other hand the Hilbert scheme of n points in $P^3$ is singular and there is a conjecture on what the monomial ideal with the largest tangent space dimension should be. By extending the combinatorial methods used in $P^2$, we give a proof of a major portion of the conjecture (in a sense we will describe). Along the way we will strengthen previous bounds on the dimension of the tangent space. This is joint (ongoing) work with Alessio Sammartano.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125268&date=2019-04-16Harmonic Analysis Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125317&date=2019-04-17
In the first part of the talk, I will outline the proof of the multilinear oscillatory integral inequality that was introduced last week. In the second part we will begin a series of lectures on a new topic, decoupling inequalities, following Bourgain-Demeter and Bourgain-Demeter-Guth.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125317&date=2019-04-17Topology Seminar (Introductory Talk), Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125265&date=2019-04-17
As context for the main talk, we will describe results of Franks and Franks-Handel in surface dynamics and state the ergodic theorem. Two- and three-dimensional dynamics are related via the notions of a global surface of section and open book decomposition, which we will introduce. To close we will discuss the ECH spectral numbers, a three-dimensional construction which can be used to study questions in surface dynamics related to those introduced at the beginning of the talk.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125265&date=2019-04-17Deformation Theory Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125254&date=2019-04-17
I will talk about a new moduli-theoretic interpretation of the spaces of framed little disks, as well as their higher-genus generalization of complex curves with parametrized boundary, as geometric objects over the rational field Q. Applications of this formalism give geometric "explainations" for several results previously proven using transcendental or analytic methods, namely formality of $E_n$ operads, Galois action on Drinfeld associators, and certain relations between "modular" periods and zeta functions proven by Hain.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125254&date=2019-04-17Conformal embedding and percolation on the uniform triangulation, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125260&date=2019-04-17
Following Smirnov’s proof of Cardy’s formula and Schramm’s discovery of SLE, a thorough understanding of the scaling limit of critical percolation on the regular triangular lattice has been achieved. Smirnorv’s proof in fact gives a discrete approximation of the conformal embedding which we call the Cardy embedding. In this talk I will present a joint project with Nina Holden where we show that the uniform triangulation under the Cardy embedding converges to the Brownian disk under the conformal embedding. Moreover, we prove a quenched scaling limit result for the critical percolation on uniform triangulations. Time permitting, I will also explain how this result fits into the the larger picture of random planar maps and Liouville quantum gravity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125260&date=2019-04-17Number Theory Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125281&date=2019-04-17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125281&date=2019-04-17From correlation to causation — measuring ad effectiveness at scale, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125235&date=2019-04-17
Everyone has had that one ad for that one pair of shoes seem to follow them everywhere they go on the internet. Why does that happen? Especially if you already bought the shoes? To make sense of this, it's worth understanding how marketers have historically measured ad effectiveness -- and why the problem is harder than it seems. Beyond improvements in measuring ad effectiveness, this talk with dive into the uniquely statistical problems we face in ad tech and some of the ways we are approaching them.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125235&date=2019-04-17Topology Seminar (Main Talk), Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125266&date=2019-04-17
An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the diffeomorphism is the mean action of the orbit. If an area-preserving annulus diffeomorphism is a rotation near the boundary of the annulus, and if its Calabi invariant is less than the maximum boundary value of the action function, then we show that the infimum of the mean action over all periodic orbits of the diffeomorphism is less than or equal to its Calabi invariant.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125266&date=2019-04-17Paris/Berkeley/Bonn/Zürich Analysis Seminar, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125271&date=2019-04-18
I will discuss a joint work with Sergiu Klainerman on the stability of Schwarzschild as a solution to the Einstein vacuum equations with initial data subject to a certain symmetry class.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125271&date=2019-04-18BIDS Data Science Lecture: Astrophysical Machine Learning, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124964&date=2019-04-18
From streaming, repeated, noisy, and distorted images of the sky, time-domain astronomers are tasked with extracting novel science as quickly as possible with limited and imperfect information. Employing algorithms developed in other fields, we have has already reached important milestones demonstrating the speed and efficacy of using ML in data and inference workflows. Now we look to innovations in learning architectures and computational approaches that are purpose-built alongside the specific domain questions. I will describe such efforts—developed in the search for Planet 9, new classes of variable sources, and for data-driven emulators—and discuss on-going efforts to imbue physical understanding into the learning process itself.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124964&date=2019-04-18Mathematics Department Colloquium/Serge Lang Undergraduate Lecture, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125066&date=2019-04-18
Topologists will say that a coffee cup is like a donut. What do they mean? Homotopy and Homology are invariants created to distinguish basic geometric structures. In this talk I will briefly talk about the history of such invariants and describe new ones that are also applicable to discrete structures like graphs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125066&date=2019-04-18'Information and Uncertainty in Data Science' Discussion Forum, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124355&date=2019-04-19
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
<br />
The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124355&date=2019-04-19Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125375&date=2019-04-19
I will describe a tropical looking algorithm computing Betti numbers (for intersection cohomology) of moduli spaces of semistable sheaves on the projective plane. This algorithm is an explicit realization of the naive idea of moving in a space of stability conditions and applying a wall-crossing formula. I will also discuss some application to some a priori unrelated question in relative Gromov-Witten theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125375&date=2019-04-19Student Probability/PDE Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125180&date=2019-04-19
We present the work of Armstrong, Cardaliaguet, and Souganidis, who prove convergence rates for stochastic homogenization using a mixture of probability techniques and PDE techniques. We discuss the metric problem, its rate of convergence, its relation to approximate correctors, and the reduction of the full problem to that of approximate correctors.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125180&date=2019-04-19Student Arithmetic Geometry Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125387&date=2019-04-19
I will discuss a paper of Maulik and Poonen on the ranks of Neron-Severi groups of geometric fibers of a smooth proper morphism of varieties over an algebraically closed field of characteristic $0$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125387&date=2019-04-19Student 3-Manifold Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125389&date=2019-04-19
We will talk about some of the basic theory of knots and links in $S^3$ with a special focus on the geometry of the complementary space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125389&date=2019-04-19Combinatorics Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125196&date=2019-04-22
The Ehrhart polynomial counts the number of lattice points in integer dilates of a lattice polytope. The h*-polynomial encodes the Ehrhart polynomial in a particular basis. In this talk we give an introduction to the method of interlacing polynomials which is a powerful tool to prove that a polynomial has only real roots and present applications to h*-polynomials of zonotopes and dilated lattice polytopes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125196&date=2019-04-22Probabilistic Operator Algebra Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122407&date=2019-04-22
The Aronszajn-Donoghue theorem provides a good understanding of the subtle theory of rank one perturbations. One of their statements consists of the mutual singularity of the singular parts of the spectral measures under rank one perturbations. For higher rank perturbations, simple examples show that the singular parts can behave more complicatedly. Nonetheless, a 'vector' version of the mutual singularity of the singular parts and a modified Aleksandrov spectral averaging prevail in the finite rank setting. Applications of these results yield further restrictions of the singular spectrum under finite rank perturbations. The presentation is based on joint work with Sergei Treil.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122407&date=2019-04-22String-Math Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125417&date=2019-04-22
3 dimensional \(N=4\) supersymmetric quantum field theories have two distinguished topological twists, called Higgs and Coulomb (though we periodically get confused about which is which). These two twists manifest very interesting mathematical objects in Lie theory and algebraic geometry, which don't seem to obviously be related, except through this bridge in QFT. I'll do my best to explain what physicists know to mathematicians, what mathematicians know to physicists, and if I fail at both, hopefully there will be some comedy value in my attempt.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125417&date=2019-04-22Arithmetic Geometry and Number Theory RTG Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125423&date=2019-04-22
Wan conjectured that the variation of zeta functions along towers of curves associated to the $p$-adic etale cohomology of a fibration of smooth proper ordinary varieties should satisfy several stabilizing properties. The most basic of these conjectures state that the genera of the curves in these towers grow in a regular way. We state and prove a generalization of this conjecture, which applies to the graded pieces of the slope filtration of an overconvergent $F$-isocrystal.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125423&date=2019-04-22Differential Geometry Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124853&date=2019-04-22
We will discuss Witten’s gauge theory approach to Jones polynomial by counting solutions to the Kapustin-Witten(KW) equations with singular boundary conditions over 4-manifolds. We will give a classification of solutions to the KW equations on $S^1\times\Sigma\times \mathbb R^+$ with $\Sigma$ a Riemann surface. We prove that all solutions to the KW equations over $S^1\times\Sigma\times \mathbb R^+$ are $S^1$ direction invariant and we give a classification of the KW monopole over $\Sigma\times R^+$ based on the Hermitian-Yang-Mills type structure of KW monopole equation. This is based on joint works with Rafe Mazzeo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124853&date=2019-04-22Tarski Lecture, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125070&date=2019-04-22
The Kepler Conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space can have density greater than that of the face-centered cubic packing. This talk will describe the history and proof of the conjecture, including early attempts to reduce the problem to a finite calculation, controversy surrounding claimed proofs, the announcement of a proof by Sam Ferguson and me more than 20 years ago, and finally a formal proof of the Kepler conjecture in the HOL Light proof assistant in 2014.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125070&date=2019-04-22Analysis and PDE Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125223&date=2019-04-22
I will present a theorem on the full finite codimension asymptotic stability of the Schwarzschild family of black holes. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125223&date=2019-04-22Seminar 217, Risk Management: CANCELLED, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122095&date=2019-04-23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122095&date=2019-04-23Student Harmonic Analysis and PDE Seminar (HADES), Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125388&date=2019-04-23
Multiphase mean curvature flow has, due to its importance in materials science, received a lot of attention over the last decades. On the one hand, there is substantial recent progress in the construction of weak solutions. On the other hand, strong solutions are—in particular in the planar case of networks—very well understood.<br />
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In this talk, after giving an overview of the topic, I will present a weak-strong uniqueness principle for multiphase mean curvature flow: as long as a strong solution to multiphase mean curvature flow exists, any distributional solution with optimal energy dissipation rate has to coincide with this solution.<br />
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In our proof we construct a suitable relative entropy functional, which in this geometric context may be viewed as a time-dependent variant of calibrations. Just like the existence of a calibration guarantees that one has found a global minimum, the existence of a “time-dependent calibration” ensures that the route of steepest descent in the energy landscape is unique and stable.<br />
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For the purpose of this talk, I will focus on two instructive model cases: a single smooth interface and a single triple junction.<br />
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This is a joint work (in progress) with Julian Fischer, Sebastian Hensel, and Thilo Simon.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125388&date=2019-04-233-Manifold Seminar, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125447&date=2019-04-23
This is an update on a similar talk given a couple of years ago. Baker and Reid asked a question about whether a tower of principal congruence covers of an arithmetic hyperbolic 3-manifold associated to powers of a prime ideal might satisfy the RFRS condition (Residually Finite Rational Solvable). A positive answer to this question implies the existence of a congruence cover that fibers over the circle. We prove that this (essentially) follows if the first principal congruence subgroup is p-torsion free, where the prime ideal divides p. Examples are known for some Bianchi groups, and now for O(4,1;Z) and for a certain complex hyperbolic surface. The O(4,1;Z) example gives infinitely many Bianchi groups with discriminant a sum of two squares having a fibered congruence cover. Joint with Matthew Stover.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125447&date=2019-04-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125420&date=2019-04-23
Why do we have the version of Galois theory that we do – why, indeed, do we have Galois theory at all? This talk traces conflicting 19th-century visions of what it would be to solve, or better to understand, polynomial equations and finds the forgotten role of Felix Klein in promoting Galois's ideas in Germany and America.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125420&date=2019-04-23Representation Theory and Mathematical Physics Seminar, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125445&date=2019-04-23
The Schur algebra is a finite dimensional algebra that connects a number of interesting topics, including the modular representation theory of the symmetric and general linear groups and category O. I will discuss joint work with Tom Braden motivated the the theory of symplectic duality in which we introduce a similar algebra for any graph or, more generally, matroid. I will also discuss more recent work in progress with Jens Eberhardt, which relates these `matroidal Schur algebras' to Braden-Licata-Proudfoot-Webster's `hypertoric category O' via categorification.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125445&date=2019-04-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125421&date=2019-04-23
This is a background talk on problems about indecomposable rank two bundles on Pn. We pay special attention to those that are limits of split bundles.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125421&date=2019-04-23Harmonic Analysis Seminar, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125467&date=2019-04-24
Decoupling inequalities express a form of orthogonality, in certain $L^p$ norms, for functions whose Fourier transforms are supported in small neighborhoods of curved submanifolds of Euclidean space. This talk will be an introduction (building on last week's pre-introduction) to the decoupling inequality of Bourgain and Demeter for paraboloids in $R^d$, for $d\ge 2$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125467&date=2019-04-24Topology Seminar (Introductory Talk), Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125315&date=2019-04-24
I will describe Khovanov's categorification of the Jones polynomial. We will talk about some applications of Khovanov homology to low-dimensional topology, such as Rasmussen's proof that the four-ball genus of the \((p,q)\) torus knot is \((p-1)(q-1)/2\). We will also talk about some directions in which the theory has been generalized.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125315&date=2019-04-24Deformation Theory Seminar, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125465&date=2019-04-24
We will discuss some of the structures related to superpotentials appearing in the work of Gaiotto, Moore and Wittenhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125465&date=2019-04-24The topologies of random real algebraic hypersufaces, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125369&date=2019-04-24
The topology of a hyper-surface in P^n(R) <br />
of high degree can be very complicated .However <br />
if we choose the surface at random there is a universal <br />
law . Little is known about this law and it appears <br />
to be dramatically different for n=2 and n>2 .<br />
There is a similar theory for zero sets of monochromatic <br />
waves which model nodal sets .<br />
Joint work with Y.Canzani and I.Wigmanhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125369&date=2019-04-24Representation Theory and Mathematical Physics Seminar, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125415&date=2019-04-24
I give an introduction to the BV-BFV formalism and discuss the setting of certain AKSZ theories. Moreover, I describe a globalization procedure using concepts of formal geometry, which extends the Quantum Master Equation for manifolds with boundary.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125415&date=2019-04-24Topology Seminar (Main Talk), Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125316&date=2019-04-24
I will describe a construction of a stable homotopy type which is a knot invariant, and whose (ordinary) homology is Khovanov homology. We will state some applications of this spatial refinement. Time permitting, we will describe further spatial refinements of other variants of Khovanov homology, such as invariants for tangles. This is joint with Robert Lipshitz and Tyler Lawson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125316&date=2019-04-24Number Theory Seminar, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125472&date=2019-04-24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125472&date=2019-04-24Tarski Lecture, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125071&date=2019-04-24
This talk will describe a broad long-term research program to make formal proofs in mathematics a practical reality. A formal proof is a mathematical proof that has been checked exhaustively by computer, on the basis of the fundamental axioms of mathematics and the primitive inference rules of logic. The field has progressed to the point that it is now possible to give formal proofs of major theorems in mathematics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125071&date=2019-04-24Applied Math Seminar, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123969&date=2019-04-25
In this talk, we will present some stochastic algorithms and numerical results for solving electromagnetic problems in nano-particles and random meta-materials. Firstly, we will present a path integral Monte Carlo method for computing magnetic polarizability tensors of nano-particles of complex geometries for material sciences applications. The method relies on a Feynman-Kac formula involving reflecting Brown motions (RBMs) and accurate computation of the local time of the RBMs using a random walk-on-spheres technique. Secondly, in order to optimize functional properties of 3-D random meta-materials (MMs), we will present a stochastic representation scheme for random MMs with volume exclusion constrains and given correlations, a fast volume integral equation electromagnetic solver for the scattering of a large number of meta-atoms of typical geometric shapes (cubes, spheres, and ellipses) in layered media, and a procedure to optimize the optical properties of the MMs. A new fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green's functions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123969&date=2019-04-25Cooperating with the Curse of Dimensionality, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125386&date=2019-04-25
The curse of dimensionality arises when analyzing high-dimensional data and non-Euclidean data, such as network data, which are ubiquitous nowadays. It causes counter-intuitive phenomena and makes traditional statistical tools less effective or inapplicable. On the other hand, some counter-intuitive phenomena might be explained by some universal patterns, which could be used to form new effective tools in dealing with high-dimensional/non-Euclidean data. In this talk, one such unique pattern is explored and applied to fundamental statistical tasks, including hypothesis testing and cluster analysis, leading to substantial improvements in conducting these tasks for high-dimensional/non-Euclidean data. Some other related topics will also be briefly discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125386&date=2019-04-25Mathematics Department Colloquium, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125446&date=2019-04-25
In recent years non-archimedean methods have shown to be a quite powerful tool in complex algebraic geometry. I shall present some of the results that can be obtained that way, proceeding from Thuiller's proof of the invariance of the homotopy type of the incidence complex to more recent results.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125446&date=2019-04-25Student Probability/PDE Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125045&date=2019-04-26
We revisit the [R. Jordan, D. Kinderlehrer, and F. Otto. The variational formulation of the Fokker-Planck equation (1998)] variational characterization of diffusion as entropic gradient flux, and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in terms of the quadratic Wasserstein metric. We obtain novel, stochastic-process versions of these features, valid along almost every trajectory of the diffusive motion in both the forward and, most transparently, the backward, directions of time, using a very direct perturbation analysis; the original results follow then simply by taking expectations. As a bonus, we derive the Cordero-Erausquin version of the so-called HWI inequality relating relative entropy, Fisher information and Wasserstein distance.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125045&date=2019-04-26Deformation Theory Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125466&date=2019-04-26
We will review the construction of generators in MF categories, following work of a Dyckerhoff, Orlov and othershttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125466&date=2019-04-26Representation Theory and Mathematical Physics Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125068&date=2019-04-26
Hurwitz numbers enumerate branched coverings of the Riemann sphere with specified branching profiles. \(\tau \)-functions of hypergeometric type for the KP and \(2D\)-Toda integrable hierarchies serve as combinatorial generating functions for weighted sums over Hurwitz numbers, with weights chosen as symmetric functions of a set of auxiliary parameters determined by a weight generating function. This talk will explain how multicurrent correlators may be used to explicitly generate weighted Hurwitz numbers as weighted polyonomials in the Taylor coefficients of the weight generating function, without any knowledge required either of symmetric group characters or the Kostka matrices relating different bases of the ring of symmetric functions. The case of rational weight generating functions will be the main illustrative example.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125068&date=2019-04-26Tarski Lecture, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125072&date=2019-04-26
In 1995, Kontsevich introduced a new form of integration, call motivic integration. From the start, the development of motivic integration has been guided by model theory, especially quantifier elimination. One particularly useful result has been a far-reaching generalization of the Ax-Kochen-Ersov transfer principle in logic to integration. This talk will give a gentle introduction to motivic integration and will highlight some applications to the Langlands program.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125072&date=2019-04-26Student 3-Manifold Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125514&date=2019-04-26
We will continue our discussion of spaces that are the complement of a knot or link in $S^3$, and then we will talk about Conway's normalization of the Alexander polynomial. If time permits, we will see the definition of the Jones polynomial via the Kauffman bracket.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125514&date=2019-04-26Combinatorics Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125373&date=2019-04-29
The branching rule for representations of the symmetric group tells us that, over a field of characteristic zero, the dimension of the irreducible representation indexed by a partition λ is given by the number of directed lattice paths from λ (though of as an integer vector) to the origin that stay inside the dominant Weyl chamber. Over a field of positive characteristic (or for Hecke algebras at roots of unity) this is no longer true, and the dimension of an irreducible is in general unknown. We will see, however, that there is a nice class of irreducibles (called calibrated, completely splittable or tame by different authors) whose dimension is given by the number of lattice paths to the origin that stay within a dilation of the fundamental alcove. Then we will provide an explicit resolution of these modules by Specht modules, whose dimensions are as in the characteristic zero case. This gives a representation-theoretic interpretation of combinatorial results of Filasetta, Krattenthaler and others. Based on joint work with C. Bowman and E. Norton.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125373&date=2019-04-29Berkeley Statistics and Machine Learning Forum, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124352&date=2019-04-29
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
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The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124352&date=2019-04-29Probabilistic Operator Algebra Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124949&date=2019-04-29
In this talk I will discuss the process of “unbounding” a topology on a vector lattice. In the $L_p$-space case this process converts the norm topology to the topology of convergence in measure . I will then discuss how unbounded topologies connect with the minimal and universal objects in the category of vector lattices, and how some of their natural properties cannot be characterized in ZFC.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124949&date=2019-04-29String-Math Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125418&date=2019-04-29
Both the Higgs bundle moduli space and the moduli space of flat connections have a natural stratification induced by a \(C^*\)-action. In both of these stratifications, each stratum is a holomorphic fibration over a connected component of complex variations of Hodge structure. While the nonabelian Hodge correspondence provides a homeomorphism between Higgs bundles and flat connections, this homeomorphism does not preserve the respective strata. The closed stratum on the Higgs bundle side is the image of the Hitchin section and the closed stratum in the space of flat connections is the space of opers. In this talk, we will show how many of the relationships between opers and the Hitchin section extend to general strata. In particular, we will show that the conformal limit identifies certain holomorphic Lagrangian subspaces of the stratifications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125418&date=2019-04-29Arithmetic Geometry and Number Theory RTG Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125444&date=2019-04-29
A basic question in the study of Galols representations is whether a mod p representation, valued in any reductive group, of the absolute Galois group of a number field admits a geometric p-adic lift. In some cases this question has a positive answer, in other cases a negative answer, and sometimes we simply don't know what to expect. Perhaps the most general setting in which one can hope for a positive result is when the number field is totally real, and the representation in question is "totally odd," generalizing Serre's notion of oddness for GL(2). I will discuss joint work with N. Fakhruddin and C. Khare on finding geometric lifts of irreducible totally odd representations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125444&date=2019-04-29Differential Geometry Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125531&date=2019-04-29
Let (X,L) be a polarized complex manifold. A good understanding of the space of Kähler metrics in the cohomology class of L is crucial to variational approach to constructing canonical metrics on X. I will discuss joint work with S. Boucksom, in which we analyze geodesic rays in (the completion of) this space, partially from a non-Archimedean point of view.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125531&date=2019-04-29Analysis and PDE Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125374&date=2019-04-29
A fundamental problem in the context of Einstein’s equations of general relativity is to understand the dynamical evolution of small perturbations of stationary black hole solutions. It is expected that there is a discrete set of characteristic frequencies that play a dominant role at late times and carry information about the nature of the black hole, much like how the normal frequencies of a vibrating guitar string play an important role in the resulting sound wave. These frequencies are called quasinormal frequencies or resonant frequencies and they are closely related to scattering resonances in the study of Schrödinger-type equations. I will consider the linear wave equation on black hole backgrounds as a toy model for Einstein’s equations and give an introduction to resonances in this setting. Then I will discuss a new method of defining and studying resonances on asymptotically flat spacetimes, developed from joint work with Claude Warnick, which puts resonances on the same footing as normal modes by showing that they are eigenfunctions of a natural operator acting on a Hilbert space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125374&date=2019-04-29Seminar 217, Risk Management: The Implication of Information Network in Market Quality and Market Reaction to Public Announcements, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122097&date=2019-04-30
This research studies the role of information network in market quality and market reaction to public announcements. We propose in this article a three-period rational noisy expected equilibrium model by taking both public and private information into account with an embedded information network structure among market traders. Closed form expressions for market reaction and market quality are derived as a function of topological structure of the network and several novel results are revealed. The trading volume and price change have different responses to network connectedness. As network connectedness increases, there is a downward trend for price change. The downward trend are decreasing which reﬂects that the market eﬃciency can not increase to inﬁnite in reality. However, the change of trading volume is uncertain because it depends on two attributes of the network, the uniformity and connectedness, it is hard to compare which one dominate another one. To the market quality, the information precision can increase market liquidity, market eﬃciency and decrease the cost of capital, network connectedness plays the same role in market eﬃciency and cost of capital, while it has a non-monotone inﬂuence towards market liquidity. And also network will suppress the eﬀect caused by disclosure.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122097&date=2019-04-303-Manifold Seminar, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125532&date=2019-04-30
Around 1990, Reshetikhin and Turaev discovered a family of 3d TQFTs whose relation to the rest of 3-manifold topology is still poorly understood. The biggest obstruction to relating these TQFTs to the rest of the 3-manifold world is that their original construction is almost entirely algebraic. For closed manifolds, Kirby and Melvin managed to relate one of these TQFTs to some classical invariants of Spin manifolds. For 3-manifolds with boundary (or, especially, surfaces with boundary), the relation of this TQFT to classical topology is trickier and not so geometrically motivated. This talk will motivate and sketch a purely topological construction of a very closely related Spin TQFT. Rather than produce a family of topological invariants from algebra, this construction produces algebra from a family of topological invariants. The general Reshetikhin-Turaev construction of TQFTs will be reviewed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125532&date=2019-04-30Student Harmonic Analysis and PDE Seminar (HADES), Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125567&date=2019-04-30
Spectral geometry aims at understanding how geometry influences the spectrum of geometrically related operators such as the Laplace operator. I will first talk about Von Neumann theory on classification of self-adjoint extensions of symmetric operators, and in particular focus on the Laplace operator on metrics with conical singularities. Then I will give a survey on how geometry (e.g. curvature and monodromy) and choice of self-adjoint extensions influence the spectrum, and discuss some results related to translation surfaces and spherical conical metrics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125567&date=2019-04-30Student Harmonic Analysis and PDE Seminar (HADES), Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125568&date=2019-04-30
Spectral geometry aims at understanding how geometry influences the spectrum of geometrically related operators such as the Laplace operator. I will first talk about Von Neumann theory on classification of self-adjoint extensions of symmetric operators, and in particular focus on the Laplace operator on metrics with conical singularities. Then I will give a survey on how geometry (e.g. curvature and monodromy) and choice of self-adjoint extensions influence the spectrum, and discuss some results related to translation surfaces and spherical conical metrics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125568&date=2019-04-30Representation Theory and Mathematical Physics Seminar, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124749&date=2019-04-30
The algebra of charged free fermions participates in the construction of classical boson-fermion correspondence and provides vertex operator realization of Schur symmetric functions. We will show how vertex operator realizations of several other famous families of symmetric functions (Hall-Littlewood polynomials, shifted Schur functions, multiparameter Schur Q-functions) can be obtained by simple modifications of operators of charged free fermions and make some notes on the corresponding versions of boson-fermion correspondence.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124749&date=2019-04-30Harmonic Analysis Seminar, May 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125533&date=2019-05-01
A short proof of the multilinear Kakeya inequality of Bennett-Carbery-Tao will be presented. This proof (due to Guth, 2015) is based on induction on scales and the Loomis-Whitney inequality, without the nonlinear heat flow of the original proof. In a future lecture, this result will serve as an ingredient in the proof of the multilinear restriction and decoupling inequalities.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125533&date=2019-05-01Topology Seminar (Introductory Talk), May 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125566&date=2019-05-01
I will start by motivating cobordism categories by recalling the notion of topological field theories. Then I will explain why “higher” categories appear naturally in this context (and what they are).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125566&date=2019-05-01Rapidly mixing random walks on matroids and related objectsidly mixing random walks on matroids and related objects, May 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125543&date=2019-05-01
A central question in randomized algorithm design is what kind of distributions can we sample from efficiently? On the continuous side, uniform distributions over convex sets and more generally log-concave distributions constitute the main tractable class. We will build a parallel theory on the discrete side, that yields tractability for a large class of discrete distributions. We will use this theory to resolve a 30-year-old conjecture of Mihail and Vazirani that matroid polytopes have edge expansion at least 1. We will also obtain simple nearly-linear time algorithms for sampling from spanning trees of a graph, and easy-to-implement algorithms for volume-based sampling.<br />
The hammer enabling these algorithmic advances is the introduction and the study of a class of polynomials, that we call completely log-concave. We can use very simple and easy-to-implement random walks to perform the task of sampling, and we will use completely log-concave polynomials to analyze the random walk. Based on joint work with Kuikui Liu, Shayan Oveis Gharan, Cynthia Vinzant.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125543&date=2019-05-01Number Theory Seminar, May 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125473&date=2019-05-01
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125473&date=2019-05-01Topology Seminar (Main Talk), May 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125544&date=2019-05-01
Lurie’s approach to the Cobordism Hypothesis builds upon a suitable higher category of cobordisms. The model of \((\infty,1)\)-categories given by complete Segal spaces (and their higher analogs) are a very natural choice for constructing cobordism categories. A drawback is that the first natural definitions only give Segal spaces, which, for high dimensions, are not complete. This follows directly from the \(s\)-cobordism theorem. In this talk, after explaining and defining the necessary notions in detail, I will explain a very simple model of cobordisms, which is a completion of the usual one. In particular it indeed is complete. This is joint work with Ulrike Tillmann.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125544&date=2019-05-01Center for Computational Biology Seminar, May 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120953&date=2019-05-01
Leveraging linkage disequilibrium to identify adaptive and disease-causing mutations<br />
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Abstract: <br />
Correlation among genotypes in human population-genetic datasets complicates the localization of both adaptive mutations and disease-causing mutations. I will describe our latest efforts to develop new methods for localizing adaptive and disease-causing mutations, motivated by (1) incorporating summary statistics at various genomic scales into selection scans, (2) bridging the gap between polygenic and omnigenic complex traits, and (3) testing for differential genetic architecture for the same trait across ancestries.<br />
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Bio: <br />
Sohini Ramachandran is Associate Professor of Ecology and Evolutionary Biology and Director of Brown University's Center for Computational Molecular Biology. During Spring 2019, she is also a Fellow in the Natural Sciences Programme at the Swedish Collegium for Advanced Study in Uppsala, Sweden. Prior to beginning her faculty appointment at Brown University in 2010, Sohini spent 3 years as a Junior Fellow at the Harvard Society of Fellows and postdoctoral fellow in Professor John Wakeley’s group at the Harvard University Department of Organismic and Evolutionary Biology. She completed her PhD in 2007 with Marcus Feldman at Stanford University’s Department of Biological Sciences. Sohini's research has been funded by the National Science Foundation and National Institutes of Health, and she was named a Pew Scholar in the Biomedical Sciences and an Alfred P. Sloan Research Fellow.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120953&date=2019-05-01Mathematics Department Colloquium, May 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125569&date=2019-05-02
I shall cover some well-known facts about hydrodynamic turbulence, and present a physically coherent view of intermittency in the energy cascade as a cascade of eddies governed by ideas of statistical mechanics. The approach presented is close to the ideas of Kolmogorov but gives a satisfactory estimate of the intermittency exponents and of the Reynolds number at the onset of turbulence. I shall also indicate why the Kolmogorov-Obukhov does not work.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125569&date=2019-05-02Gammage Seminar, May 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125624&date=2019-05-03
This reports on joint work with Umut Varolgunes. In 2007, Entov and Polterovich introduced the notion of heavy and superheavy subsets of symplectic manifolds. We define and study a Floer-theoretic analogue of this notion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125624&date=2019-05-03'Information and Uncertainty in Data Science' Discussion Forum, May 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124356&date=2019-05-03
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
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The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124356&date=2019-05-03Dissertation Talk: Approximate counting, phase transitions and geometry of polynomials, May 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125497&date=2019-05-03
In classical statistical physics, a phase transition is understood by studying the geometry (the zero-set) of an associated polynomial (the partition function). In this talk I will show that one can exploit this notion of phase transitions algorithmically, and conversely exploit the analysis of algorithms to understand phase transitions. As applications, I will give efficient deterministic approximation algorithms (FPTAS) for counting q-colorings, and for computing the partition function of the Ising model.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125497&date=2019-05-03Arithmetic Geometry and Number Theory RTG Seminar, May 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125574&date=2019-05-03
Given a curve of genus at least $2$ over a number field, Faltings' theorem tells us that its set of rational points is finite. Provably computing the set of rational points remains a major open problem, as does the question of whether the number of rational points can be uniformly bounded. We will survey some recent progress and ongoing work using the Chabauty–Kim method, which uses the fundamental group to construct $p$-adic analytic functions that vanish on the set of rational points. In particular, we present a new proof of Faltings' theorem for superelliptic curves over the rational numbers (due to joint work with Jordan Ellenberg), and a conditional generalization of the Chabauty–Kim method to number fields and higher dimensions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125574&date=2019-05-03Student 3-Manifold Seminar, May 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125626&date=2019-05-03
In this talk, I will try to go through all the ways I am aware of that one can define the Alexander polynomial. To name a few: Alexander's original definition, the Fox calculus, the Conway potential function, polynomial extrapolation of $U_q(\mathfrak {sl}(n))$ quantum invariants, Reidemeister torsion, the Burau representation of braid groups, Alexander representations of the knot quandle, and knot Floer homology.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125626&date=2019-05-03Combinatorics Seminar, May 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125468&date=2019-05-06
Both LLT polynomials and k-Schur functions were derived from the study of Macdonald polynomials, and have proved to be fruitful areas of study. A conjecture due to Haglund and Haiman states that k-bandwidth LLT polynomials expand positively into k-Schur functions. This is trivial in the case k=1 and has been recently proved for k=2. In this talk, I will present a proof for the case k=3. To this end, I will introduce a new computational method for establishing linear relations among LLT polynomials.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125468&date=2019-05-06String-Math Seminar, May 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125623&date=2019-05-06
It has been understood for some time now that many highlights of Lie theory, such as the representation-theoretic theory of special functions, or the Kazhdan–Lusztig theory, have a natural extension to a much broader setting, the boundaries of which are yet to be explored. In this extension, the focus is shifting from a group \(G\) to various classes of algebraic varieties that possess the key features of \(T^*G/B\). While there are some proposal about what should replace a Lie algebra, root systems, etc., it is less clear what should be the group, or multiplicative analog of these structures. Reflecting the nature of the field, the talk will combine a review of established partial results with unsubstantiated speculations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125623&date=2019-05-06Northern California Symplectic Geometry Seminar, May 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125572&date=2019-05-06
Let $(M,\omega )$ be a closed symplectic manifold. Consider a closed symplectic submanifold $D$ whose homology class is a positive multiple of the Poincare dual of $[\omega ]$. The complement of $D$ can be given the structure of a Liouville manifold, with skeleton $S$. We prove that $S$ cannot be displaced from itself inside $M$ by a Hamiltonian isotopy if we assume that $c_1(M)=0$. Under the same assumption, we also prove that Floer theoretically essential Lagrangians in $M$ have to intersect $S$. These results are related to an understanding of the notions heavy and superheavy in terms of relative symplectic cohomology. Ongoing joint work with Dmitry Tonkonog.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125572&date=2019-05-06Differential Geometry Seminar, May 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125422&date=2019-05-06
A spherical surface with $n$ conical singularities is a surface $S$ with cone points $x_1, \dots ,x_n$ and a metric $g$, such that $g$ has curvature 1 on the complement $S \setminus (x_1,...,x_n)$ and has a conical singularity of angle $2\pi (\theta _i)$ at each $x_i$. Moduli spaces of spherical metrics with fixed angles are intriguing objects. Up to very recently the most basic questions about these spaces were open, in particular it was not known for which angles such spaces are non-empty, whether they can be disconnected, whether they project surjectively to the moduli space of curves with $n$ marked points. I'll speak about solutions of such questions, the talk is based on a joint work with Gabirele Mondello.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125422&date=2019-05-06Northern California Symplectic Geometry Seminar, May 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125573&date=2019-05-06
The discovery of the Jones polynomial in the early 80s was the beginning of "quantum topology": the introduction of various invariants which, in one sense or another, arise from quantum mechanics and quantum field theory. There are many mathematical constructions of these invariants, but they all share the defect of being first defined in terms of a knot diagram, and only subsequently shown by calculation to be independent of the presentation. As a consequence, the geometric meaning has been somewhat opaque.<br />
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By contrast, in the physics literature, there is a geometric story: Witten showed that the invariants can be extracted from a 3d quantum field theory, and he later showed that this quantum field theory can be found as a boundary condition in string theory. However, it has been difficult to translate these ideas into mathematics, because they a priori depend on infinite dimensional integrals which have no mathematically rigorous definition.<br />
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In the talk I will explain how just enough of the open topological string theory can be made mathematically precise so as to give a manifestly geometric interpretation of the skein relation: it is a boundary term which must be set to zero in order to invariantly count holomorphic curves with boundary. As a consequence one finds that the HOMFLY polynomial (a generalization of the Jones polynomial) is a count of holomorphic curves in a certain 6-dimensional setting which is invariantly and geometrically constructed from the three-dimensional topology.<br />
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This talk draws from the paper “Skeins on Branes” written with Tobias Ekholm.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125573&date=2019-05-06Harmonic Analysis Seminar, May 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125611&date=2019-05-08
Multilinear restriction estimates are an important tool in the proof of the decoupling inequality for the paraboloid. This talk will introduce and provide a heuristic proof of a multilinear restriction estimate, relying on the multilinear Kakeya inequality discussed in last week's talk. If time permits, attention will be given to applications to decoupling and multilinear decoupling (the latter being an ingredient in a proof of the former).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125611&date=2019-05-08Topology Seminar (Introductory Talk), May 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125648&date=2019-05-08
Scissor congruence theory of polytopes is an old subject going back to 19th century. One of its first major achievements was appearance of so-called Dehn invariant. This mysterious invariant could be properly understood and generalized in the context of the theory of mixed Hodge structures of mixed Tate type. I will explain this relation and show some applications to hyperbolic geometry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125648&date=2019-05-08BIDS Data Science Lecture: Hate speech, algorithms, and digital connectivity, May 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125241&date=2019-05-08
The Online Hate Index (OHI) is a research partnership between UC Berkeley’s D-Lab and Google Jigsaw that seeks to improve society's understanding of online hate speech (from sources such as YouTube, Reddit, Twitter and other social media sites), including its prevalence over time, variation across regions and demographics, our ability to measure it through crowdsourcing and algorithms, and how to influence it through historical or future interventions. Through a combination of citizen science and machine learning, the team is developing a nuanced measurement methodology that decomposes hate speech into various constituent components, enabling it to be transformed into a continuous “hate speech scale,” making it easier to rate, evaluate and understand than a single omnibus question (i.e. "is this comment hate speech?").<br />
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The project is setting new standards for the data science of hate speech, with goals to 1) establish a theoretically-grounded definition of hate speech inclusive of research/policies/practice, 2) develop and apply a multi-component labeling instrument, 3) create a new crowdsourcing tool to scalably label comments, 4) curate an open, reliable multi-platform labeled hate speech corpus, 5) grow existing data and tool repositories within principles of replicable and reproducible research, enabling greater transparency and collaboration, 6) create new knowledge through ethical online experimentation (and citizen science), and 7) refine AI models. The research team includes Geoff Bacon (Linguistics Ph.D. candidate); Nora Broege (Postdoc at Rutgers University); Chris Kennedy (Biostatistics Ph.D. student, BIDS Fellow); and Alexander Sahn (Political Science Ph.D. candidate).<br />
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Ultimately, we seek to understand the causal mechanisms for intervention and evaluation, while defending free speech. A new open-source platform - to be used by the Anti-Defamation League and other advocacy organizations - will make these resources (along with policy recommendations) available to educate the public and grow the larger data science / citizen science community.<br />
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BIDS Data Science Lectures are open to the entire campus community.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125241&date=2019-05-08Last Passage percolation: modulus of continuity and the slow bond problem, May 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125652&date=2019-05-08
The talk has two parts. In the first part we will speak on the modulus of <br />
continuity in Poissonian last passage percolation, a model lying in the <br />
KPZ universality class. In the second part we speak on the “slow bond” <br />
model, where Totally Asymmetric Simple Exclusion Process (TASEP) on <br />
$\mathbb{Z}$ (a model which can be thought to simulate a one-way traffic <br />
movement) is modified by adding a slow bond at the origin, that is, particles <br />
at the origin wait longer before making jumps. A conjectural description <br />
of properties of invariant measures of TASEP with a slow bond at the <br />
origin was provided in Liggett's 1999 book . We establish Liggett’s <br />
conjectures and in particular show that TASEP with a slow bond at the <br />
origin, starting from step initial condition, converges in law to an <br />
invariant measure that is asymptotically close to product measures with <br />
different densities far away from the origin towards left and right. Joint work with Alan Hammond, Allan Sly and Riddhipratim Basu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125652&date=2019-05-08Arithmetic Geometry and Number Theory RTG Seminar, May 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125588&date=2019-05-08
Deligne's "Weil II" paper includes a far-reaching conjecture to the effect that for a smooth variety on a finite field of characteristic $p$, for any prime $\ell $ distinct from $p$, $\ell $-adic representations of the etale fundamental group do not occur in isolation: they always exist in compatible families that vary across $\ell $, including a somewhat more mysterious counterpart for $\ell =p$ (the "petit camarade cristallin"). We explain what such an object is; indicate the role of the Langlands correspondence for function fields in the approach to Deligne's conjecture; and report on prior and ongoing work towards the conjecture (including results of Deligne, Drinfeld, Abe-Esnault, and the speaker).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125588&date=2019-05-08Topology Seminar (Main Talk), May 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125649&date=2019-05-08
I will explain how to construct a rational elliptic surface out of every non-Euclidean tetrahedra. This surface "remembers" the trigonometry of the tetrahedron: the length of edges, dihedral angles and the volume can be naturally computed in terms of the surface. The main property of this construction is self-duality: the surfaces obtained from the tetrahedron and its dual coincide. This leads to some unexpected relations between angles and edges of the tetrahedron. For instance, the cross-ratio of the exponents of the spherical angles coincides with the cross-ratio of the exponents of the perimeters of its faces. The construction is based on relating mixed Hodge structures, associated to the tetrahedron and the corresponding surface.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125649&date=2019-05-08Paris/Berkeley/Bonn/Zürich Analysis Seminar, May 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125625&date=2019-05-09
Multiphase mean curvature flow has, due to its importance in materials science, received a lot of attention over the last decades. In this talk, I will show how the gradient-flow structure allows to prove convergence results for several numerically relevant schemes, including phase-field models and thresholding schemes in codimensions one and two. The methods combine basic geometric measure theory, the theory of gradient flows in metric spaces, and multiscale analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125625&date=2019-05-09Applied Math Seminar, May 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125570&date=2019-05-09
The facetious and self-serving title refers to four approaches for Navier-Stokes simulations. The first involves the analysis, numerical analysis, and an efficient implementation strategy for a recently proposed fractional Laplacian closure model that accounts for Richardson pair dispersion observed in turbulent flows. The second is the exploitation of accurate and widely applicable ensemble methods in settings in which multiple inputs need to be processed, as may be the case for uncertainty quantification, reduced-order modeling, and control and optimization. The third addresses the lack of regularity of solutions and the resultant loss of accuracy of approximations in the case of white or weakly correlated additive noise forcing. The fourth involves filtered spectral viscosity and hierarchical finite element methods for regularized Navier-Stokes equations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125570&date=2019-05-09Special Seminar, May 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125671&date=2019-05-09
Carmine Emanuele Cella, assistant professor in music and technology at CNMAT, will present work done in the last years in searching good signal representations that permit high-level manipulation of musical concepts. After the definition of a geometric approach to signal representation, the theory of sound-types and its application to music will be presented. Finally, recent research on assisted orchestration will be shown and some possible musical applications will be proposed, with connections to deep learning methods.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125671&date=2019-05-09Applied Math Seminar, May 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125571&date=2019-05-10
We use the canonical examples of fractional Laplacian and peridynamics equations to discuss their use as models for nonlocal diffusion and mechanics, respectively, via integral equations with singular kernels. We then proceed to discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus to define weak formulations in function space settings. In particular, we discuss the recently developed asymptotically compatible families of discretization schemes. Brief forays into examples and extensions are made, including obstacle problems and wave problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125571&date=2019-05-10Solving Hard Computational Problems using Oscillator Networks, May 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125647&date=2019-05-10
Over the last few years, there has been considerable interest in Ising machines, ie, analog hardware for solving difficult (NP hard/complete) computational problems effectively. <br />
We present a new way to make Ising machines using networks of coupled self-sustaining nonlinear oscillators. <br />
Our scheme is theoretically rooted in a novel result that connects the phase dynamics of coupled oscillator systems with the Ising Hamiltonian.<br />
We show that oscillators can be designed to take on a binary phase, and a network of such binary oscillators has phase dynamics evolving naturally towards local minima of the Ising Hamiltonian. <br />
Two simple additional steps (ie, adding noise, and tuning the binarization strength up and down) enable the network to find excellent solutions of Ising problems. <br />
We evaluate our method on Ising versions of the MAX-CUT problems, showing that it improves on previously published results on several benchmark problems. <br />
Our scheme, which is amenable to realization using many kinds of oscillators from different physical domains, is particularly well suited for CMOS, in which it offers significant practical advantages over previous techniques for making Ising machines. <br />
We have demonstrated several working hardware prototypes using CMOS electronic oscillators, built on breadboards and PCBs, implementing Ising machines consisting of 4, 8, 32, 64 and 240 spins.<br />
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In this talk, we will also go over my other Ph.D. work that has led to the development of oscillator-based Ising machines. <br />
In particular, we show that binary oscillators are not only useful for Ising, but can also be used to devise Finite State Machines for general-purpose Boolean computation with phase-based logic encoding, extending a scheme originally proposed by John von Neumann.<br />
We also briefly show my other research topics that have enabled the above work on oscillators, particularly those on the modelling of multi-domain nonlinear devices/systems, and those on advanced simulation analyses (eg, oscillator-specific analyses based on linear periodically time-varying system theory).<br />
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At the end of this talk, there will be a lab demonstration of a prototype oscillator-based Ising machine of 240 spins with programmable couplings.<br />
The prototype is built using off-the-shelf components on PCBs, roughly 10"x6"x4" in size, and interfaces with a laptop through USB.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125647&date=2019-05-10String-Math Seminar, May 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125419&date=2019-05-13
Wilson loops are important observables in gauge theory. In this talk, we study half-BPS Wilson loops of a large class of five dimensional supersymmetric quiver gauge theories with 8 supercharges, in a nontrivial instanton background. The Wilson loops are codimension 4 defects of the quiver gauge theory, and their interaction with self-dual instantons is captured by a 1d ADHM quantum mechanics. We compute the partition function as its Witten index. It turns out that we can understand the 5d physics in 3d gauge theory terms. This comes about from so-called gauge/vortex duality; namely, we study the vortices on the Higgs branch of the 5d theory, and reinterpret its partition function from the point of view of the vortices. This perspective has an advantage: it has a dual description in terms of "deformed" Toda Theory on a cylinder, in the Coulomb gas formalism. We show that the gauge theory partition function is equal to a (chiral) correlator of the deformed Toda Theory, with stress tensor and higher spin operator insertions. We derive all the above results from type IIB string theory, compactified on a resolved \(ADE\) singularity \(X\) times a cylinder with punctures. The 5d quiver gauge theory arises as the low energy limit of a system of D5 branes wrapping various two-cycles of \(X\), the Wilson loops are D1 branes, and the duality to Toda theory emerges after introducing additional D3 branes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125419&date=2019-05-13Representation Theory and Mathematical Physics Seminar, May 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125416&date=2019-05-16
The reduced phase space of the Poisson Sigma Model (PSM) comes equipped with a symplectic groupoid structure, when the worldsheet is a disk and the target Poisson structure is integrable. In this talk we describe an extension of this construction when we consider surfaces with arbitrary genus, obtaining the abelianization of the original groupoid. We will also describe the obstructions for smoothness of such abelianization, in terms of the extended monodromy groups. This can be seen as a generalization of the Hurewicz theorem to Lie groupoids and Lie algebroids. Joint work with Rui Fernandes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125416&date=2019-05-16Analysis and PDE Seminar, May 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125769&date=2019-05-20
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^2$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration including Weyl laws; in each case obtaining quantitative improvements over the known bounds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125769&date=2019-05-20