Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsUniform rates of the Glivenko-Cantelli convergence and their use in approximating Bayesian inferences, Aug 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118859&date=2018-08-22
This talk deals with suitable quantifications in approximating a probability measure by an “empirical” random probability measure \hat p_n, depending on the first n terms of a sequence \{\xi_i\}_{i\ge1}<br />
of random elements. In the first part, we study the range of oscillation near zero of the p-Wasserstein distance d(p) .... See the link for the full abstract. <br />
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Based on joint work with Emanuele Dolera.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118859&date=2018-08-22Rerandomization and Regression Adjustment, Aug 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118917&date=2018-08-22
Randomization is a basis for the statistical inference of treatment effects without assumptions on the outcome generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. In his seminal work Design of Experiments, R. A. Fisher suggested blocking on discrete covariates in the design stage and conducting the analysis of covariance (ANCOVA) in the analysis stage. In fact, we can embed blocking into a wider class of experimental design called rerandomization, and extend the classical ANCOVA to more general regression-adjusted estimators. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference-in-means estimator in the analysis stage. We argue that practitioners should always consider using a combination of rerandomization and regression adjustment. Under the randomization-inference framework, we establish a unified theory allowing the designer and analyzer to have access to different sets of covariates. We find that asymptotically (a) for any given estimator with or without regression adjustment, using rerandomization will never hurt either the sampling precision or the estimated precision, and (b) for any given design with or without rerandomization, using our regression-adjusted estimator will never hurt the estimated precision. To theoretically quantify these statements, we propose two notions of optimal regression-adjusted estimators and measure the additional gains of the designer and analyzer based on the sampling precision and estimated precision. This is a joint work with Xinran Li.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118917&date=2018-08-22Topology Seminar (Main Talk), Aug 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119096&date=2018-08-22
The question in the title is akin to asking where the equation of motion of a free falling object $a + bt + 1/2 gt^2$ in 3-space come from? then discovering that the "objects fall with constant acceleration" rule. Similarly, we derive Seiberg-Witten equations (which also have a linear part and a quadratic part) from the deformation equations of an "isotropic associative submanifold" of a complex $G_2$ Manifold. For this, we will define the notion of complex $G_2$ manifold and notion of complexification of a $G_2$ manifold (this is a joint work with Ustun Yildirim).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119096&date=2018-08-22Arithmetic Geometry and Number Theory RTG Seminar, Aug 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118919&date=2018-08-27
Pre-talk: Completed cohomology, as defined by Calegari and Emerton, is a natural candidate for general spaces of p-adic automorphic forms. I'll give a motivated introduction to completed cohomology and the p-adic Langlands program in the setting of modular curves.<br />
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Main talk: I'll discuss some new vanishing theorems for completed cohomology, building on previous work of Scholze and Shen. The proofs involve a fun combination of perfectoid methods and more classical Shimura variety techniques, which I'll try to explain. This is joint work in progress with Christian Johansson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118919&date=2018-08-27Differential Geometry Seminar, Aug 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118888&date=2018-08-27
A gravitational instanton is a noncompact complete hyperkähler 4-manifold with faster than quadratic curvature decay. In this talk, I will discuss the classification of gravitational instantons. This is a joint work with Xiuxiong Chen.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118888&date=2018-08-27Analysis/PDE Seminar, Aug 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118690&date=2018-08-27
First I will describe a new pseudodifferential calculus for (pseudo-)Riemannian spaces, which in our opinion (my, D.Siemssen's and A.Latosiński's) is the most appropriate way to study operators on such a manifold. I will briefly describe its applications to computations of the asymptotics the heat kernel and Green's operator on Riemannian manifolds. Then I will discuss analogous applications to Lorentzian manifolds, relevant for QFT on curved spaces. I will mention an intriguing question of the self-adjointness of the Klein-Gordon operator. I will describe the construction of the (distinguished) Feynman propagator on asymptotically static spacetimes. I will show how our pseudodifferential calculus can be used to compute the full asymptotics around the diagonal of various inverses and bisolutions of the Klein-Gordon operator.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118690&date=2018-08-27Seminar 217, Risk Management: Is motor insurance ratemaking going to change with telematics and semi-autonomous vehicles?, Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118738&date=2018-08-28
Many automobile insurance companies offer the possibility to monitor driving habits and distance driven by means of telematics devices installed in the vehicles. This provides a novel source of data that can be analysed to calculate personalised tariffs. For instance, drivers who accumulate a lot of miles should be charged more for their insurance coverage than those who make little use of their car. However, it can also be argued that drivers with more miles have better driving skills than those who hardly use their vehicle, meaning that the price per mile should decrease with distance driven. The statistical analysis of a real data set by means of machine learning techniques shows the existence of a gaining experience effect for large values of distance travelled, so that longer driving should result in higher premium, but there should be a discount for drivers that accumulate longer distances over time due to the increased proportion of zero claims. We confirm that speed limit violations and driving in urban areas increase the expected number of accident claims. We discuss how telematics information can be used to design better insurance and to improve traffic safety. Predictive models provide benchmarks of the impact of semi-autonomous vehicles on insurance rates.<br />
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This talk will cover the award winning paper on semiautonomous vehicle insurance presented in the International Congress of Actuaries in Berlin, June, 2018, which is under revision in Accident Analysis and Prevention and it will also include the contents of a paper entitled “The use of telematics devices to improve automobile insurance rates”, accepted in Risk Analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118738&date=2018-08-283-Manifold Seminar, Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119173&date=2018-08-28
Jeffrey and Weitsman showed that the space of (projective) representations of a surface group into $SU(2)$ admits a perfect Morse function. We'll discuss a direct proof of this by Michael Thaddeus, and an extension to representations of a punctured surface with prescribed holonomy about the punctures.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119173&date=2018-08-28Student Harmonic Analysis and PDE Seminar (HADES), Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119230&date=2018-08-28
I will describe joint work with Jared Wunsch on propagation of singularities for some semiclassical Schrodinger equations where the potential is conormal to a hypersurface, with applications to logarithmic resonance-free regions. Semiclassical singularities of a given strength propagate across the hypersurface up to a threshold depending on the regularity of the potential and the singularities along certain backwards branching bicharacteristics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119230&date=2018-08-28Probabilistic Operator Algebra Seminar, Aug 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118887&date=2018-08-28
The order structure of a Banach lattice gives rise to several natural convergences. In this talk we begin by reviewing the essential results on Banach lattices, and then discuss recent research on basic sequences in such spaces. The basic sequences we are interested in are those whose partial sums converge not only in norm, but also in order. We show that this class of bases can be characterized by a natural modification of the standard basis inequality, and discuss some of the more unexpected corollaries. This is a joint project with V.G. Troitsky ; the results extend and unify those of A. Gumenchuk, O. Karlova and M. Popov, Order Schauder bases in Banach lattices, J. Funct. Anal. (2015).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118887&date=2018-08-28Topology Seminar (Introductory Talk), Aug 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118996&date=2018-08-29
We introduce Teichmuller space in various respects in terms of conformal structures, hyperbolic structures and representations. We briefly describe natural metrics on Teichmuller space, and useful functions to study the geometry of Teichmuller space. Finally, we introduce energy functional and convexity, plurisubharmonicity of energy functionals.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118996&date=2018-08-29Spectrum of random non-selfadjoint operators, Aug 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118915&date=2018-08-29
The spectrum of non-selfadjoint operators can be highly unstable even under very small perturbations. This phenomenon is referred to as "pseudospectral effect". <br />
Traditionally this pseudosepctral effect was considered a drawback since it can be the source of immense numerical errors, as shown for instance in the works of L. N. Trefethen. However, this pseudospectral effect can also be the source of many new insights. A line of works by Hager, Bordeaux-Montrieux, Sjöstrand, Christiansen and Zworski exploits the pseudospectral effect to show that the (discrete) spectrum of a large class of non-selfadjoint pseudo-differential operators subject to a small random perturbation follows a Weyl law with probability close to one. <br />
In this talk we will discuss the local statistics of the eigenvalues of such operators (in dimension one). That is the distribution of the eigenvalues on the scale of their average spacing. We will show that the pseudospectral effect leads to a partial form of universality of the local statistics of the eigenvalues. <br />
This is joint work with Stéphane Nonnenmacher (Université Paris-Sud).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118915&date=2018-08-29Topology Seminar (Main Talk), Aug 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118997&date=2018-08-29
We prove the plurisubharmonicity of energy functional on Teichmuller space for the smooth harmonic maps from a fixed Riemannian manifold into Riemann surfaces. We also give a strict convexity of the energy functional along the Weil-Petersson geodesics. This is a joint work with Wan and Zhang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118997&date=2018-08-29Likelihood Ratio Test for Stochastic Block Models with Bounded Degrees, Aug 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119156&date=2018-08-29
A fundamental problem in network data analysis is to test whether a network contains statistical significant communities. We study this problem in the stochastic block model context by testing H0: Erdos-Renyi model vs. H1: stochastic block model. This problem serves as the foundation for many other problems including the testing-based methods for determining the number of communities and community detection. Existing work has been focusing on growing-degree regime while leaving the bounded-degree case untreated. Here, we propose a likelihood ratio type procedure based on regularization to test stochastic block models with bounded degrees. We derive the limiting distributions as power Poisson laws under both null and alternative hypotheses, based on which the limiting power of the test is carefully analyzed. The joint impact of signal-to-noise ratio and the number of communities on the asymptotic results is also unveiled. The proposed procedures are examined by both simulated and real-world network datasets. Our proofs depend on the contiguity theory for random regular graphs developed by Janson (1995). This talk is based on a joint work with Mingao Yuan and Zuofeng Shang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119156&date=2018-08-29Stochastic Gradient Descent: Strong convergence guarantees -- without parameter tuning, Aug 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119284&date=2018-08-30
Stochastic Gradient Descent is the basic optimization algorithm behind powerful deep learning architectures which are becoming increasingly omnipresent in society. However, existing theoretical guarantees of convergence rely on knowing certain properties of the optimization problem such as maximal curvature and noise level which are not known a priori in practice. Thus, in practice, hyper parameters of the algorithm such as the stepsize are tuned by hand before training, taking days or weeks. In this talk, we discuss a modification of Stochastic Gradient Descent with an adaptive "on the fly" step size update known as AdaGrad which is used in practice but until now did not come with any theoretical guarantees. We provide the first such guarantees, showing that Stochastic Gradient Descent with AdaGrad converges to a near-stationary point of a smooth loss function, at a rate which nearly matches the "oracle" rate as if the curvature of the loss function and noise level on the stochastic gradients were known in advance. We also demonstrate its favorable empirical performance on deep learning problems compared to pre-tuned state-of-the-art algorithms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119284&date=2018-08-30Mathematics Department Colloquium / Applied Math Seminar / Statistics Seminar, Aug 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119345&date=2018-08-30
Stochastic Gradient Descent is the basic optimization algorithm behind powerful deep learning architectures which are becoming increasingly omnipresent in society. However, existing theoretical guarantees of convergence rely on knowing certain properties of the optimization problem such as maximal curvature and noise level which are not known a priori in practice. Thus, in practice, hyper parameters of the algorithm such as the stepsize are tuned by hand before training, taking days or weeks. In this talk, we discuss a modification of Stochastic Gradient Descent with an adaptive "on the fly" step size update known as AdaGrad which is used in practice but until now did not come with any theoretical guarantees. We provide the first such guarantees, showing that Stochastic Gradient Descent with AdaGrad converges to a near-stationary point of a smooth loss function, at a rate which nearly matches the "oracle" rate as if the curvature of the loss function and noise level on the stochastic gradients were known in advance. We also demonstrate its favorable empirical performance on deep learning problems compared to pre-tuned state-of-the-art algorithms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119345&date=2018-08-30Student Probability/PDE Seminar, Aug 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119172&date=2018-08-31
I will talk about the general aspects about the microcanonical ensembles given by several constraints. In contrast to the single constraint, interesting phase transition and localization phenomenon can happen. The general theory to study this structure, using the large deviation principle, will be given.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119172&date=2018-08-31Logic Colloquium, Aug 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119175&date=2018-08-31
Neologicism emerges in the contemporary debate in philosophy of mathematics with Wright's book Frege's \textit {Conception of Numbers as Objects} (1983). Wright's project was to show the viability of a philosophy of mathematics that could preserve the key tenets of Frege's approach, namely the idea that arithmetical knowledge is analytic. The key result was the detailed reconstruction of how to derive, within second order logic, the basic axioms of second order arithmetic from Hume's Principle \[(\textrm {HP})\quad \forall C,D\,\big (\sharp (C) = \sharp (D)\leftrightarrow C\cong D\big )\] (and definitions). This has led to a detailed scrutiny of so-called abstraction principles, of which Basic Law V \[(\textrm {BLV})\quad \forall C,D \,\big (ext(C) = ext(D) \leftrightarrow \forall x\,(C(x)\leftrightarrow D(x))\big )\] and HP are the two most famous instances. As is well known, Russell proved that BLV is inconsistent. BLV has been the only example of an abstraction principle from (monadic) concepts to objects giving rise to inconsistency, thereby making it appear as a sort of monster in an otherwise regular universe of abstraction principles free from this pathology. We show that BLV is part of a family of inconsistent abstractions. The main result is a theorem to the effect that second-order logic formally refutes the existence of any function $F$ that sends concepts into objects and satisfies a "part-whole" relation. In addition, we study other properties of abstraction principles that lead to formal refutability in second-order logic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119175&date=2018-08-31Student Arithmetic Geometry Seminar, Aug 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119482&date=2018-08-31
This is the first meeting of the student arithmetic geometry seminar. Like past semesters, this will be a "paper seminar": Participants will choose a paper from a list I will distribute and give a talk about it. In this first meeting, we will go over some of the practical aspects of the seminar after which I will discuss some results about the problem of reconstructing a variety from categorical data such as the derived category, categories of sheaves, line bundles etc.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119482&date=2018-08-31Seminar 217, Risk Management: On Optimal Options Book Execution Strategies with Market Impact, Sep 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118739&date=2018-09-04
We consider the optimal execution of a book of options when market impact is a driver of the option price. We aim at minimizing the mean-variance risk criterion for a given market impact function. First, we develop a framework to justify the choice of our market impact function. Our model is inspired from Leland’s option replication with transaction costs where the market impact is directly part of the implied volatility function. The option price is then expressed through a Black– Scholes-like PDE with a modified implied volatility directly dependent on the market impact. We set up a stochastic control framework and solve an Hamilton–Jacobi–Bellman equation using finite differences methods. The expected cost problem suggests that the optimal execution strategy is characterized by a convex increasing trading speed, in contrast to the equity case where the optimal execution strategy results in a rather constant trading speed. However, in such mean valuation framework, the underlying spot price does not seem to affect the agent’s decision. By taking the agent risk aversion into account through a mean-variance approach, the strategy becomes more sensitive to the underlying price evolution, urging the agent to trade faster at the beginning of the strategy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118739&date=2018-09-043-Manifold Seminar, Sep 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119485&date=2018-09-04
We'll continue to discuss a perfect Bott-Morse function on certain $SU(2)$ representation varieties associated to punctured surfaces following Thaddeus. The variety is a symplectic manifold, with a certain $U(1)$ Hamiltonian action on a subset which is a moment map for the Morse function away from the maximum and minimum critical levels. From this one may deduce that the Morse function is perfect.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119485&date=2018-09-04Student Harmonic Analysis and PDE Seminar (HADES), Sep 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119667&date=2018-09-04
Solitary waves are waves on the surface of the water which keep a constant profile and which move with constant velocity. Two longstanding open problems have been whether such waves exist in deep water in the presence of either gravity or surface tension, but not both. This talk will provide the answers to both of these problems in two space dimensions. This is joint work with Mihaela Ifrim.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119667&date=2018-09-04Probabilistic Operator Algebra Seminar, Sep 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118889&date=2018-09-04
Study of operator smoothness was initiated in the 50's. Since then it has substantially expanded in scope and methods in response to various problems in perturbation theory. The first order operator differentiability is well understood. In particular, it is known that the set of functions differentiable with respect to the Schatten $S^p$-norms, $p$ >1, can be described in terms of smoothness properties of scalar functions and is wider than the set of functions differentiable with respect to the operator norm or $S^1$-norm. The higher order differentiability was known for a limited set of functions, We will discuss new results that significantly extend the sets of higher order Frechet and Gateaux $S^p$-differentiable functions, $p$ >1. Our results are based on recent advances in theory of generalized multilinear Schur multipliers. The talk is based on joint work with Christian Le Merdy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118889&date=2018-09-04Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119305&date=2018-09-04
In the first hour, we discuss the problem of interpolation for curves in projective space: When does there exist a curve of degree d and genus g passing through n general points in $\mathbb P^r$?http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119305&date=2018-09-04Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119306&date=2018-09-04
In the second hour, we discuss the Maximal Rank Conjecture, a conjecture formulated originally by Severi in 1915 which prescribes a relationship between the "shape" of the parametric and Cartesian equations of curves in projective space — that is, which gives the Hilbert function of a general curve of genus g, embedded in $\mathbb P^r$ via a general linear series of degree d. We then explain how results on the interpolation problem can be leveraged to prove this conjecture.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119306&date=2018-09-04Topology Seminar (Introductory Talk), Sep 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119549&date=2018-09-05
To each oriented surface one can associate two algebras: commutative coordinate ring of the character variety of the fundamental group and noncommutative skein algebra. Both algebras enjoy the action of the mapping class group of the surface by automorphisms. In my introductory talk I will define both algebras mentioned above and show how they are related to each other. I will then describe a one-parameter deformation of the skein algebra of torus known as the Spherical Double Affine Hecke Algebra (DAHA) and review some applications to the theory of symmetric polynomials.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119549&date=2018-09-05Concentration of the spectral norm of Erdös-Rényi random graphs, Sep 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119057&date=2018-09-05
In this joint work with Shahar Mendelson and Nikita Zhivotovsky, we study concentration properties of the largest eigenvalue of the <br />
adjacency matrix of a G(n,p) random graph. We use inequalities for higher moments of general functions of independent random variables and delocalization of the eigenvectors to prove nonasymptotic <br />
concentration inequalities. In particular, we prove that the largest eigenvalue is uniformly concentrated for the entire random graph <br />
process.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119057&date=2018-09-05AdaPT: An interactive procedure for multiple testing with side information, Sep 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119471&date=2018-09-05
We consider the problem of multiple hypothesis testing with generic side information: for each hypothesis we observe both a p-value and some predictor encoding contextual information about the hypothesis. For large-scale problems, adaptively focusing power on the more promising hypotheses (those more likely to yield discoveries) can lead to much more powerful multiple testing procedures. We propose a general iterative framework for this problem, called the Adaptive p-value Thresholding (AdaPT) procedure, which adaptively estimates a Bayes-optimal p-value rejection threshold and controls the false discovery rate (FDR) in finite samples. At each iteration of the procedure, the analyst proposes a rejection threshold and observes partially censored p-values, estimates the false discovery proportion (FDP) below the threshold, and either stops to reject or proposes another threshold, until the estimated FDP is below α. Our procedure is adaptive in an unusually strong sense, permitting the analyst to use any statistical or machine learning method she chooses to estimate the optimal threshold, and to switch between different models at each iteration as information accrues. <br />
This is joint work with Lihua Lei.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119471&date=2018-09-05Topology Seminar (Main Talk), Sep 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119550&date=2018-09-05
Spherical Double Affine Hecke Algebra can be viewed as a noncommutative \((q,t)\)-deformation of the \(SL(N,C)\) character variety of the fundamental group of a torus. This deformation inherits major topological property from its commutative counterpart, namely Mapping Class Group of a torus \(SL(2,Z)\) acts by atomorphisms of DAHA. In my talk I will define a genus two analogue of \(A_1\) spherical DAHA and show that the Mapping Class Group of a closed genus two surface acts by automorphisms of such algebra. I will then show that for special values of parameters \(q,t\) satisfying \(q^n t^2=1\) for some nonnegative integer n this algebra admits finite dimensional representations. I will conclude with discussion of potential applications to TQFT and knot theory.<br />
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Based on arXiv:1704.02947 joint with Sh. Shakirovhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119550&date=2018-09-05Applied Math Seminar, Sep 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119347&date=2018-09-06
Optimization problems governed by partial differential equations are ubiquitous in modern science, engineering, and mathematics. They play a central role in optimal design and control of multiphysics systems, data assimilation, and inverse problems. However, as the complexity of the underlying PDE increases, efficient and robust methods to accurately compute the objective function and its gradient become paramount. To this end, I will present a globally high-order discretization of PDEs and their quantities of interest and the corresponding fully discrete adjoint method for use in a gradient-based PDE-constrained optimization setting. The framework is applied to solve a slew of optimization problems including the design of energetically optimal flapping motions, the design of energy harvesting mechanisms, and data assimilation to dramatically enhance the resolution of magnetic resonance images. In addition, I will demonstrate that the role of optimization in computational physics extends well beyond these traditional design and control problems. I will introduce a new method for the discovery and high-order accurate resolution of shock waves in compressible flows using PDE-constrained optimization techniques. The key feature of this method is an optimization formulation that aims to align discontinuous features of the solution basis with the discontinuities in the solution. The method is demonstrated on a number of one- and two-dimensional transonic and supersonic flow problems. In all cases, the framework tracks the discontinuity closely with curved mesh elements and provides accurate solutions on extremely coarse meshes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119347&date=2018-09-06Student Probability/PDE Seminar, Sep 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119666&date=2018-09-07
I will talk about the general aspects of the microcanonical ensembles given by several constraints. In contrast to the single constraint, interesting phase transition and localization phenomenon can happen. The general theory to study this structure, using the large deviation principle, will be given.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119666&date=2018-09-07Combinatorics Seminar, Sep 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119661&date=2018-09-10
We generalize the Varchenko matrix of a hyperplane arrangement to oriented matroids. We show that the celebrated determinant formula for the Varchenko matrix, first proved by Varchenko, generalizes to oriented matroids. It follows that the determinant only depends on the matroid underlying the oriented matroid and analogous formulas hold for cones in oriented matroids. We follow a proof strategy for the original Varchenko formula first suggested by Denham and Hanlon. Besides several technical lemmas this strategy also requires a topological result on supertopes which is of independent interest.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119661&date=2018-09-10Differential Geometry Seminar, Sep 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118918&date=2018-09-10
A fundamental result of Donaldson-Sun states that noncollapsed Gromov-Hausdorff limits of polarized Kähler manifolds, with two-sided Ricci curvature bounds, are normal projective varieties. We extend their approach to the setting where only a lower bound for the Ricci curvature is assumed. More precisely, we show that noncollapsed Gromov-Hausdorff limits of polarized Kähler manifolds, with Ricci curvature bounded below, are normal projective varieties. In addition the metric singularities are precisely given by a countable union of analytic subvarieties. This is a joint work with Gabor Szekelyhidi.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118918&date=2018-09-10Arithmetic Geometry and Number Theory RTG Seminar, Sep 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119346&date=2018-09-10
In the early 1990s Ribet observed that the classical mod l multiplicity one results for modular curves, which are a consequence of the q-expansion principle, fail to generalize to Shimura curves. Specifically he found examples of Galois representations which occur with multiplicity 2 in the mod l cohomology of a Shimura curve with discriminant pq and level 1.<br />
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I will describe a new approach to proving multiplicity statements for Shimura curves, using the Taylor-Wiles-Kisin patching method (which was shown by Diamond to give an alternate proof of multiplicity one in certain cases), as well as specific computations of local Galois deformation rings done by Shotton. This allows us to re-interpret and generalize Ribet's result. I will prove a mod l "multiplicity $2^k$" statement in the minimal level case, where k is a number depending only on local Galois theoretic data.<br />
<br />
Time permitting I will also describe joint work (in progress) with Jack Shotton, in which we use these techniques to prove new cases of Ihara's Lemma for Shimura curves, which are not covered by the work of Diamond and Taylor.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119346&date=2018-09-10Analysis and PDE Seminar, Sep 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119671&date=2018-09-10
We prove new quantitative additive energy estimates for a large class of porous measures which include, for example, all Hausdorff measures of Ahlfors-David subsets of the real line of dimension strictly between 0 and 1. We are able to obtain improved quantitative results over existing additive energy bounds for Ahlfors-David sets by avoiding the use of inverse theorems in additive combinatorics and instead opting for a more direct approach which involves the use of concentration of measure inequalities. We discuss some connections with Bourgain's sum-product theorem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119671&date=2018-09-10Seminar 217, Risk Management: Capacity constraints in earning, and asset prices before earnings announcements, Sep 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118096&date=2018-09-11
This paper proposes an asset pricing model with endogenous allocation of constrained learning capacity, that provides an explanation for abnormal returns before the scheduled release of information about firms, such as quarterly earnings announcements. In equilibrium investors endogenously focus their learning capacity and acquire information about stocks with upcoming announcements, resulting in excess price movements during this period. I show cross-sectional heterogeneity in stock returns and institutional investors' information demand before quarterly earnings announcements that are consistent with the model. The results suggest that limited information acquisition capacity, and investors' optimal allocation response can play a significant role in asset price movements before firms' scheduled announcements.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118096&date=2018-09-113-Manifold Seminar, Sep 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119757&date=2018-09-11
We'll continue to discuss a result of Frankel that moment maps from circle actions on symplectic manifolds give rise to perfect Bott-Morse functions via Smith theory (the localization theorem). We'll also discuss the Goldman symplectic form on moduli spaces of representations of surface groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119757&date=2018-09-11Student Harmonic Analysis and PDE Seminar (HADES), Sep 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119668&date=2018-09-11
I will show the Stable/Unstable Manifold Theorem for hyperbolic dynamical systems (maps and flows) which describes long time dynamics in a neighborhood of a given trajectory. Time permitting, I will also give examples of hyperbolic dynamical systems such as geodesic flows on manifolds of negative curvature and dispersive billiards. This talk will follow (a subset) of the notes https://arxiv.org/abs/1805.11660http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119668&date=2018-09-11Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119483&date=2018-09-11
In this expository talk, we discuss from an elementary point of view how one approaches studying the geometry of moduli spaces of curves. We begin with classical examples of how one can prove that some moduli spaces are unirational. At the opposite extreme, following ideas of Harris, Mumford, Eisenbud and Farkas, we then explain how one can reduce proving that moduli spaces are of general type to the study of carefully chosen effective divisors on them.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119483&date=2018-09-11Probabilistic Operator Algebra Seminar, Sep 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119670&date=2018-09-11
In the 40's Wielandt and Wintner proved that the commutator of two bounded operators can never equal the identity. Four decades later Popa gave a quantitative version of this result by showing that, if the commutator of two bounded operators is close to the identity, then the norm of these operators is bounded below by half of the logarithm of the reciprocal of the distance between the commutator and the identity. In a recent paper, using only basic tools in operator theory, Terence Tao showed that Popa's bound is almost tight. In this talk we will review this proof.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119670&date=2018-09-11Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119484&date=2018-09-11
Following work of Farkas, in order to prove that the moduli spaces of curves of genus 22 (respectively, 23) are of general type, it suffices to prove that not every curve in them admits a morphism to projective 6-space of degree 25 (respectively, 26) whose image lies on a quadric. We describe a proof of this statement via a degeneration argument, combining ideas from the Eisenbud-Harris theory of limit linear series and the more recent theory of linked linear series. This is joint work with Fu Liu, Montserrat Teixidor i Bigas, and Naizhen Zhang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119484&date=2018-09-11Universality Results for Kinetically Constrained Spin Models in Two Dimensions, Sep 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119300&date=2018-09-12
Kinetically constrained models (KCM) are reversible interacting particle systems on Z^d with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and non-monotone) counterpart of the family of cellular automata known as U-bootstrap percolation. KCM also display some of the peculiar features of the so-called ``glassy dynamics'', and as such, they are extensively used in the physics literature to model the liquid-glass transition, a major and longstanding open problem in condensed matter physics.<br />
We consider two-dimensional KCM with update rule U and focus on proving universality results for the mean infection time of the origin, in the same spirit as those recently established in the setting of U-bootstrap percolation by Bollobas, Smith and Uzzell and Bollobas, Duminil-Copin, Morris and Smith. <br />
We first identify what we believe are the correct universality classes, which turn out to be different from those of U-bootstrap percolation. We then prove universal upper bounds on the mean infection time within each class, which we conjecture to be sharp up to logarithmic corrections. In certain cases, including all supercritical models, and the well-known Duarte model, our conjecture has recently been confirmed. In fact, in these cases, our upper bound is sharp up to a constant factor in the exponent.<br />
For certain classes of update rules, it turns out that the infection time of the KCM diverges much faster than for the corresponding U-bootstrap process when the equilibrium density of infected sites goes to zero. This is due to the occurrence of energy barriers which determine the dominant behavior for KCM, but which do not matter for the monotone bootstrap dynamics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119300&date=2018-09-12Number Theory Seminar, Sep 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119758&date=2018-09-12
We will discuss saturated Dieudonne complexes and the Cartier criterion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119758&date=2018-09-12How to estimate the mean of a random vector?, Sep 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119356&date=2018-09-12
Given n independent, identically distributed copies of a random<br />
vector, one is interested in estimating the expected value. Perhaps<br />
surprisingly, there are still open questions concerning this very<br />
basic problem in statistics. The goal is to construct estimators<br />
that are close to the true mean with high probability, with respect to<br />
some given norm. In this talk we are primarily interested<br />
in non-asymptotic sub-Gaussian estimates. We introduce the<br />
“median-of-means tournament” and show its optimal behavior.<br />
This talk is based on joint work with Shahar Mendelson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119356&date=2018-09-12Applied Math Seminar, Sep 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119845&date=2018-09-13
Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speedup, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. A new space–time reduced order model, the ST-GNAT method, for nonlinear dynamical systems will be introduced as well as the traditional methods, such as the DEIM and GNAT methods. The ST-GNAT method applies a space–time least-squares Petrov–Galerkin projection and space–time gappy POD approach to reduce both the dimensionality and complexity of the system. An attractive error bound associated with the ST-GNAT method and several compelling numerical results will be shown. One drawback of the ST-GNAT method is the computationally expensive offline phase where solution and nonlinear term bases as well as corresponding sample elements are constructed. To reduce the offline cost, the SNS method is developed. In contrast to the traditional hyper-reduction techniques where collection of nonlinear term snapshots is required, the SNS method completely avoids the use of the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis. Furthermore, it avoids an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119845&date=2018-09-13Mathematics Department Colloquium, Sep 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119665&date=2018-09-13
A lot of problems of classical mechanics lead us to the study of the orientation and area preserving diffeomorphisms of surfaces. Among their invariant sets, the simplest ones are the periodic orbits, but more curious invariant sets often exist : Cantor subsets. We will introduce the setting and explain why such invariant Cantor sets often exist. We will focus on two kinds of them: the horseshoes and Denjoy sets and explain that in some sense, they are linked but different.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119665&date=2018-09-13Student Probability/PDE Seminar, Sep 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119907&date=2018-09-14
It is well-known that diffusions with gradient drifts exhibit metastable behavior. The large deviation estimates of Wentzel-Freidlin and classical Eyring-Kramers Formula give a precise description for such metastable behavior. For non-gradient models, the large-deviation techniques are still applicable, though no rigorous analog of Eyring-Kramers Formula is available. In this talk I give an overview of the existing results and conjectures for general metastable diffusions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119907&date=2018-09-14Logic Colloquium, Sep 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120046&date=2018-09-14
In practice, an algebraic difference equation (of $N$ variables) is given by a set Σ of polynomials in the variables $\{ x_{i,j} ~:~ 1 \leq i \leq N, j \in \mathbb N \}$ and one looks for sequences of $N$-tuples of numbers $((a_{1,j})_{j=0}^\infty , …, (a_{N,j})_{j=0}^\infty )$ as solutions in the sense that for each $P \in \Sigma $, the equations $P(a_{1,j}, …, a_{n,j}; a_{1,j+1}, …, a_{N,j+1}; …; a_{1,d+j}, …, a_{N,d+j}) = 0$ hold for all $j \in \mathbb N$. Read more algebraically, difference equations may be understood as atomic formulae in the language of difference rings, the language of rings augmented by a function symbol for the difference operator, and we seek the solutions in the ring of sequences treated as a difference ring by interpreting the difference operator as a shift.<br />
<br />
The theory of difference fields, that is, of fields equipped with a distinguished endomorphism, has a model companion and the theory of this model companion is known to be decidable and to admit quantifier elimination in a reasonable expansion of the language of difference rings. We set out to extend the model theory of difference fields to produce algorithms to test for the solvability of difference equations in sequence rings and to solve the elimination problem for such difference equations.<br />
<br />
Remarkably, the theory of such difference rings is undecidable, already in low quantifier complexity. However, we were able to adapt the methods behind the axiomatization of the theory of difference closed fields to produce efficient algorithms to solve both the consistency checking and the elimination problems for difference equations in sequence rings. Even more remarkably, ultraproducts of Frobenius automorphisms play a crucial role in verifying the correctness of our algorithms,<br />
<br />
(This is a report on joint work with Alexey Ovchinnikov and Gleb Pogudin [available at arXiv:1712.01412] and an on-going project with them joined by Wei Li.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120046&date=2018-09-14Student Arithmetic Geometry Seminar, Sep 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119983&date=2018-09-14
This is a survey talk on the paper “Cohomology of p-adic Stein spaces” by Colmez, Dospinescu and Niziol. Drinfeld half-spaces are a p-adic analogue of the complex upper half-plane, and our goal is to describe p-adic (pro-)etale cohomology of these rigid analytic spaces in terms of Steinberg representations of the general linear group. In this talk, I will explain several key ingredients in their computation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119983&date=2018-09-14Combinatorics Seminar, Sep 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119662&date=2018-09-17
The classical volume polynomial in algebraic geometry measures the degrees of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial for matroids, give a complete combinatorial formula, and show that it is a valuation under matroid polytope subdivisions. For a realizable matroid, we thus obtain an explicit formula for the classical volume polynomial of the associated wonderful compactification; in particular, we obtain another formula for volumes of generalized permutohedra. We then introduce a new invariant called the volume of a matroid as a particular specialization of its volume polynomial, and discuss its algebro-geometric and combinatorial properties in connection to graded linear series on blow-ups of projective spaces.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119662&date=2018-09-17String-Math Seminar, Sep 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120047&date=2018-09-17
Gukov, Putrov and Vafa postulated the existence of some 3-manifold invariants, obtained by counting BPS states in the \(3d\), \(N=2\) theory \(T[M_3]\). The GPV invariants take the form of power series converging in the unit disk, and whose radial limits at the roots of unity give the Witten-Reshetikhin-Turaev invariants. Furthermore, these power series have integer coefficients, and should admit a categorification. An explicit formula for the power series exists for negative definite plumbings. In this talk I will explain what should be the analogue of the GPV invariants for manifolds with torus boundary (such as knot complements), and propose a Dehn surgery formula for these invariants. The formula is conjectural, but it can be made explicit in the case of knots given by negative definite plumbings with an unframed vertex. This is joint work (in progress) with Sergei Gukov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120047&date=2018-09-17Differential Geometry Seminar, Sep 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119841&date=2018-09-17
Suppose $(X, \omega )$ is a Kähler manifold induced by an ample line bundle $(L, X)$. We introduce $L^p$-type Finsler structures on the space of holomorphic sections of $L^k$, and show that the resulting metric spaces quantize the $L^p$-Mabuchi metric structures on the space of Kähler metrics, up to their completion. This is joint work with C.H. Lu and Y.A. Rubinstein.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119841&date=2018-09-17Arithmetic Geometry and Number Theory RTG Seminar, Sep 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119986&date=2018-09-17
We will describe how the crystalline cohomology of a supersingular K3 surface gives rise to certain one-parameter families of K3 surfaces, which we call supersingular twistor spaces. Our construction relies on the special behavior of $p$-torsion classes in the Brauer group of a supersingular K3 surface, as well as techniques coming from the study of derived categories and Fourier–Mukai equivalences. As applications, we find new proofs of Ogus’s crystalline Torelli theorem and Artin’s conjecture on the unirationality of supersingular K3 surfaces. These results are new in small characteristic.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119986&date=2018-09-17Analysis and PDE Seminar, Sep 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119908&date=2018-09-17
The AdS instability conjecture is a conjecture about the initial value problem for the Einstein vacuum equations with a negative cosmological constant. It states that there exist arbitrarily small perturbations to the initial data of the AdS spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions on conformal infinity, lead to the formation of black holes after sufficiently long time. In the recent years, a vast amount of numerical and heuristic works have been dedicated to the study of this conjecture, focusing mainly on the simpler setting of the spherically symmetric Einstein–scalar field system.<br />
<br />
In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein–massless Vlasov system. The construction of the unstable family of initial data will require working in a low regularity setting, carefully designing a family of initial configurations of localised Vlasov beams and estimating the exchange of energy taking place between interacting beams over long period of times. Time permitting, I will briefly discuss how the main ideas of the proof can be extended to more general matter fields, including the Einstein–scalar field system.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119908&date=2018-09-17Seminar 217, Risk Management: Nonstandard Analysis and its Application to Markov Processes, Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118740&date=2018-09-18
Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in probability theory as well as stochastic processes. Nonstandard analysis allows construction of a single object - a hyperfinite probability space - which satisfies all the first order logical properties of a finite probability space, but which can be simultaneously viewed as a measure-theoretical probability space via the Loeb construction. As a consequence, the hyperfinite/measure duality has proven to be particularly in porting discrete results into their continuous settings.<br />
<br />
In this talk, for every general-state-space continuous-time Markov process satisfying appropriate conditions, we construct a hyperfinite Markov process to represent it. Hyperfinite Markov processes have all the first order logical properties of a finite Markov process. We establish ergodicity of a large class of general-state-space continuous-time Markov processes via studying their hyperfinite counterpart. We also establish the asymptotical equivalence between mixing times, hitting times and average mixing times for discrete-time general-state-space Markov processes satisfying moderate condition. Finally, we show that our result is applicable to a large class of Gibbs samplers and a large class of Metropolis-Hasting algorithms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118740&date=2018-09-183-Manifold Seminar, Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120065&date=2018-09-18
We'll discuss the symplectic structure on representation varieties of surfaces. Then we'll discuss certain Hamiltonian actions on subsets determined by twists along simple curves.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120065&date=2018-09-18Student Harmonic Analysis and PDE Seminar (HADES), Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120143&date=2018-09-18
Consider the trilinear form for twisted convolution on $\mathbb R^{2d}$: $$\mathcal T_t(\mathbf f):=\iint f_1(x)f_2(y)f_3(x+y)e^{it\sigma (x,y)}dxdy,$$ where σ is a symplectic form and $t$ is a real-valued parameter. It is known that in the case $t\neq 0$ the optimal constant for twisted convolution is the same as that for convolution, though no extremizers exist. Expanding about the manifold of triples of maximizers and $t=0$ we prove a sharpened inequality for twisted convolution with an arbitrary antisymmetric form in place of σ.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120143&date=2018-09-18Probabilistic Operator Algebra Seminar, Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119174&date=2018-09-18
We describe a family of groups whose von Neumann algebras satisfy the following rigidity phenomenon: all tensor decompositions of $L(\Gamma )$ into II$_1$ factors necessarily arise from direct product decompositions of the group Γ. This class includes many iterated amalgamated free product groups such as right-angled Artin groups, Burger-Mozes groups, Higman group, integral two-dimensional Cremona groups. As a consequence, we obtain several new examples of groups that give rise to prime factors.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119174&date=2018-09-18Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119844&date=2018-09-18
Green's conjecture says that vanishing syzgies of a canonical curve is equivalent to the non-existence of certain linear series on the curve. Turning things around, we might hope that many syzygies imply the existence of many linear systems. In this talk I will survey our knowledge on syzygies of canonical curves and then report on work of Hanieh Keneshlou, who used this approach to study the scheme of curves of genus 11 with several maps of degree 6 to $\mathbb P^1$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119844&date=2018-09-18Data and sustainability science and practice, Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120008&date=2018-09-18
The energy-information nexus has become a key tool and research area in efforts aimed at decarbonizing energy systems, enabling and operating the 'smart grid', which I will argue encompasses the utility-scale system, mini-grids, and off-grid energy systems. In this talk we will review a range of theoretical models and practical tools where data science, machine learning, and human-machine interfaces have launched or enabled clean energy and energy justice (energy access and socially progressive energy choices) that would not have been possible previously. I will also highlight key opportunities for data science for sustainable energy options in California, China, and Africa.<br />
<br />
The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120008&date=2018-09-18Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119843&date=2018-09-18
We study curves in $\mathbb P^3$ lying on hypersurfaces that arise as images of “general” maps from smooth surfaces. We describe the numerical invariants of a large class of curves on these surfaces, and study the families of such curves in the Hilbert scheme.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119843&date=2018-09-18Topology Seminar (Introductory Talk), Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120063&date=2018-09-19
We'll introduce the curve complex of a surface & motivate it via its connections to hyperbolic 3-manifolds and to Teichmuller theory. The goal of this intro talk will be to discuss some of its geometric properties, on both large and small scales.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120063&date=2018-09-19TAP free energy, spin glasses, and variational inference., Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119297&date=2018-09-19
We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as ‘Z2 synchronization’. Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free energy, instead of the mean field (MF) free energy. We prove that this identification is correct, provided the ferromagnetic bias is larger than a constant (i.e. the noise level is small enough in synchronization). Namely, we prove that the scaled l2 distance between any low energy local minimizers of the TAP free energy and the mean of the Gibbs measure vanishes in the large size limit. Our proof technique is based on upper bounding the expected number of critical points of the TAP free energy using the Kac-Rice formula.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119297&date=2018-09-19Representation Theory and Mathematical Physics Seminar, Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120144&date=2018-09-19
Carlsson and Mellit introduced the Dyck path algebra and its polynomial representation, which was used to prove some important conjectures in algebraic combinatorics. I will define this algebra and construct its action on the equivariant K-theory of certain smooth strata in the flag Hilbert schemes of points on the plane. In this presentation, the fixed points of torus action correspond to generalized Macdonald polynomials and the the matrix elements of the operators have explicit combinatorial presentation. The talk is based on a joint work with Erik Carlsson and Anton Mellit.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120144&date=2018-09-19Number Theory Seminar, Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119985&date=2018-09-19
We will discuss strict Dieudonné complexes, completions of Dieudonné complexes, Dieudonné algebras, and the De Rham complex.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119985&date=2018-09-19Correcting Bias in Eigenvectors of Financial Covariance Matrices, Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119956&date=2018-09-19
There is a source of bias in the sample eigenvectors of financial covariance matrices, when unchecked, distorts weights of minimum variance portfolios and leads to risk forecasts that are severely biased downward. Recent work with Lisa Goldberg and Alex Shkolnik develops an eigenvector bias correction. Our approach is distinct from the regularization and eigenvalue shrinkage methods found in the literature. We provide theoretical guarantees on the improvement our correction provides as well as estimation methods for computing the optimal correction from data.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119956&date=2018-09-19Topology Seminar (Main Talk), Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120064&date=2018-09-19
The k-curve graph of an orientable surface S with negative Euler characteristic is a graph whose vertices correspond to (homotopy classes of) essential simple closed curves on S, and whose edges correspond to pairs of curves that geometrically intersect at most k times. For any surface with genus at least 3, we prove that the automorphism group of the 1-curve graph is isomorphic to the extended mapping class group; this resolves a conjecture of Schaller from 2000. More generally, we prove the same result for the k-curve graph so long as the absolute value of the Euler characteristic of S is at least 1000+k. This represents joint work with Yassin Chandran, Marissa Loving, Roberta Shapiro, Rob Oakley, and Sunny Yang Xiao.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120064&date=2018-09-19Center for Computational Biology Seminar, Sep 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119117&date=2018-09-19
Title: Two-phase differential expression analysis for single cell RNA-seq<br />
<br />
Abstract: Single-cell RNA-sequencing (scRNA-seq) has brought the study of the transcriptome to higher resolution and makes it possible for scientists to provide answers with more clarity to the question of ‘differential expression’. Specifically, it allows us to observe binary (On/Off) as well as continuous (the amount of expression) regulations. We present a method, SC2P, that identifies the phase of expression a gene is in, by taking into account of both cell- and gene-specific contexts, in a model-based and data-driven fashion. We then identify two forms of transcription regulation: phase transition, and magnitude tuning. We demonstrate that compared with existing methods, SC2P provides substantial improvement in sensitivity without sacrificing the control of false discovery, as well as better robustness. The ability to separately detect different forms of differential expression provides better interpretation of the nature of expression regulation. <br />
<br />
Bio:<br />
Dr. Zhijin (Jean) Wu is Associate Professor of Biostatistics at Brown University. She received her PhD in Biostatistics from Johns Hopkins in 2005 and has been a faculty at Brown since then. Her research interest is in statistical methods for analyzing gene expression and methylation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119117&date=2018-09-19Paris/Berkeley/Bonn/Zürich Analysis Seminar, Sep 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120066&date=2018-09-20
Wave turbulence is the study of the evolution of the statistics of random waves. Weak turbulence corresponds to taking an equation, coming from hydrodynamics or quantum mechanics, which is weakly nonlinear (that is we let its nonlinearity go to zero in a certain regime). One aim of this talk is to present the first aspects of the theory of weak turbulence from a mathematical physics point of view, explain which intrinsically nonlinear behavior it describes, its link with resonances and the growth of Sobolev norms. We will then present some rigorous results and perspectives. One aim is to introduce the computational tool of Feynmann diagrams in this context, its relevance and importance in fully developing the mathematical study of weak turbulence.<br />
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We will discuss a joint work with Nikolay Tzvetkov and an ongoing project with Zaher Hani.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120066&date=2018-09-20Mathematics Department Colloquium, Sep 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120044&date=2018-09-20
I will discuss the topology of a space of stable tropical curves of genus g with volume 1. The reduced rational homology of this space is canonically identified with the top weight cohomology of $M_g$ and also with the homology of Kontsevich's graph complex. As one application, we show that $H^{4g-6}(M_g)$ is nonzero for infinitely many $g$. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of a recent theorem of Willwacher, that homology of the graph complex vanishes in negative degrees, using the identifications above and known vanishing results for $M_g$. Joint work with M. Chan and S. Galatius.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120044&date=2018-09-20Combinatorics Seminar, Sep 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119663&date=2018-09-24
We consider the problem of when the difference of two ribbon Schur functions is a single Schur function. We prove that this near-equality phenomenon occurs in fourteen infinite families and we conjecture that these are the only possible cases. Towards this converse, we prove that under certain additional assumptions the only instances of near-equality are among our fourteen families. In particular, we prove that our first ten families are a complete classification of all cases where the difference of two ribbon Schur functions is a single Schur function whose corresponding partition has at most two parts at least 2. We also provide a framework for interpreting the remaining four families and we explore some ideas towards resolving our conjecture in general. We also determine some necessary conditions for the difference of two ribbon Schur functions to be Schur-positive.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119663&date=2018-09-24String-Math Seminar, Sep 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120247&date=2018-09-24
We explain how quantum affine algebras can be used to systematically construct "exotic" t-structures. One of the application is to obtain exotic t-structures on certain convolution varieties defined using affine Grassmannians (these varieties play an important role in the geometric Langlands program, knot homology constructions, the coherent Satake category etc.) As a special case we also recover the exotic t-structures of Bezrukavnikov-Mirkovic on Springer resolutions in type A. This is joint work with Clemens Koppensteiner.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120247&date=2018-09-24Differential Geometry Seminar, Sep 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120045&date=2018-09-24
I will discuss a new construction of families of Ricci-flat Kähler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding singular fibration from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds. This is joint work with Hans-Joachim Hein, Song Sun, and Ruobing Zhang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120045&date=2018-09-24Arithmetic Geometry and Number Theory RTG Seminar, Sep 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120248&date=2018-09-24
It is a classical theorem of Max Noether that the (geometric) gonality of a smooth plane curve of degree $d$ is $d-1$, and all minimal degree maps come from projection from a point on the curve. Debarre and Klassen proved an arithmetic strengthening of this result when the curve is defined over a number field: if $d \geq 8$, there are only finitely many algebraic points with residue degree strictly less than $d-1$. I will discuss extensions of this result to sufficiently ample curve classes on any surface with trivial irregularity. This is joint work with Geoffrey Smith.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120248&date=2018-09-24Seminar 217, Risk Management: A Deep Learning Investigation of One-Month Momentum, Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118741&date=2018-09-25
The one-month return reversal in equity prices was first documented by Jedadeesh (1990), who found that there was a highly significant negative serial correlation in the monthly return series of stocks. This is in contrast to the positive serial correlation of the annual stock returns. Explanations for this effect differ, but the general consensus has been that the trailing one-month return includes a component of overreaction by investors. Since 1990, the one-month return reversal effect has decayed substantially, which has led others to refine it. Asness, Frazzini, Gormsen, and Pedersen (2017) refine this idea by adjusting MAX5 (the average of the five highest daily returns over the trailing month) for trailing volatility. They define a measure SMAX (scaled MAX5), which is the MAX5 divided by the trailing month daily return volatility. SMAX is designed to capture lottery demand in excess of volatility. They show that SMAX has an even stronger one-month return reversal than trailing month return.<br />
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In this talk, I first replicate the results of Jedadeesh and Asness as benchmark models. I confirm that SMAX outperforms simple return reversal over the test period 1993-2017. However, the effectiveness of SMAX declines substantially over the test period. Using an enhanced combination of return statistics, I improve upon SMAX. I further improve upon SMAX by applying Neural Networks to trailing daily active returns. Note that all of these signals decay substantially in effectiveness over the common test period 1998-2017.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118741&date=2018-09-253-Manifold Seminar, Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120264&date=2018-09-25
We'll continue to discuss the symplectic structure on representation varieties of surfaces after Goldman (and Atiyah-Bott). Then we'll discuss certain Hamiltonian actions on subsets determined by twists along simple curves.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120264&date=2018-09-25Student Harmonic Analysis and PDE Seminar (HADES), Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120146&date=2018-09-25
Colin de Verdière and Saint-Raymond have recently found a fascinating connection between modeling of internal waves in stratified fluids and spectral theory of 0th order pseudodifferential operators on compact manifolds. The purpose of this talk is to motivate that connection and then explain challenges in spectral theory of 0th order operators, with and without viscosity. Some numerical simulations will illustrate how hyperbolic dynamics of certain classical flows results in concentration of velocities. A sketch of mathematics behind it will then be provided.<br />
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The talk is based on a short paper with S Dyatlov which resulted from a "groupe de travail" this winter in Berkeley, with inputs from T de Poyferre and T Laux.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120146&date=2018-09-25Probabilistic Operator Algebra Seminar, Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119842&date=2018-09-25
On the (p,1) Lorentz scale of normed ideals of compact operators, the Macaev ideal is the end at infinity. From a perturbation point of view the Macaev ideal is related to entropy (Kolmogorov-Sinai dynamical entropy and Avez entropy of random walks on groups), while finite p is related to Hausdorff dimension p. For discrete groups, connections to supramenability have appeared via the regular representation. Also properties of commutants mod the Macaev ideal and of associated exotic coronas will be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119842&date=2018-09-25Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119982&date=2018-09-25
I will present recent joint work with David Jensen, using tropicalization of linear series on chains of loops to verify two outstanding cases of the strong maximal rank conjecture and prove that certain divisor classes on $M_{22}$ and $M_{23}$ are represented by effective divisors. This completes Farkas’s program to show that these moduli spaces are of general type. An alternate proof in characteristic zero, using limit linear series, was subsequently discovered by Liu, Osserman, Teixidor, and Zhang, and I will also discuss relations between the two approaches.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119982&date=2018-09-25Machine Learning Panel, Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120147&date=2018-09-25
The Berkeley Master of Financial Engineering Program invites you to join us on September 25 at UC Berkeley's Haas School of Business for a Machine Learning Panel in the Spieker Forum of Chou Hall. Industry veterans will discuss applications of machine learning within their firms / industries and the state of the field.<br />
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The Haas School of Business is located on the UC Berkeley campus at 2220 Piedmont Avenue, Berkeley, CA 94720.<br />
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Schedule:<br />
3:30 PM Registration<br />
4:00 PM Program Begins: Panel Discussion and Q&A<br />
5:15 PM Reception and Networking (Refreshments will be served)<br />
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Panelists: <br />
- Laurent El Ghaoui - Professor, EECS and IEOR; Berkeley Artificial Intelligence Research; Co-Founder, SumUp Analytics<br />
- Xin Heng - Senior Director, Data, Punchh<br />
- Bulent Kiziltan - Head of Deep Learning, Aetna<br />
- Stephen Malinak - Chief Data and Analytics Officer, TruValue Labs<br />
- Mike Ryerson - Senior Researcher, The Voleon Group<br />
- Frank Xia - Data Scientist, Opendoorhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120147&date=2018-09-25Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Sep 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119987&date=2018-09-25
I’ll begin with a discussion of the classification of vector bundles on P1 and explain what natural cohomology means in this context. Then I’ll consider the case of vector bundles on P1 x P1. In general vector bundles on surfaces are more complicated but a useful tool allows one to reduce many problems about vector bundles to questions of linear algebra. This is the theory of monads. I’ll discuss monads and show how they are used to prove a conjecture of Eisenbud and Scheryer about vector bundles on P1 x P1 with natural cohomology.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119987&date=2018-09-25GRASP Seminar, Sep 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120273&date=2018-09-26
Continuing from last week, we define "universal R-matrices" of Hopf algebras and the braiding structure of categories provided. This defines actions of the braid groups $B_n$ as morphisms of modules. We finally construct the RT invariants, as functors from the tangle category to these, and compute the very simplest examples using two methods. Lastly we provide references to the literature about categorifying some of these notions: there are higher braid groups $T(k,n)$ generalizing $B_n=T(1,n)$, and there are braided monoidal 2-categories.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120273&date=2018-09-26Topology Seminar (Introductory Talk), Sep 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120311&date=2018-09-26
We will study the deformation space of hyperbolic structures on a cusped hyperbolic three-manifold M and review Thurston’s theory of hyperbolic Dehn filling. We will then explore the real projective deformations of M and the local structure of the SL(4,R) character variety as a preview of the main talk.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120311&date=2018-09-26Stability of geodesics in the Brownian map, Sep 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120101&date=2018-09-26
The Brownian map is a random non-differentiable surface, homeomorphic to the sphere, which was first identified as a scaling limit of random planar maps (Le Gall 2011 and Miermont 2011). More recently its connections with quantum gravity were established (Miller and Sheffield 2016). In this talk we show that the cut locus of the Brownian map is continuous almost everywhere, and discuss other features of its rich geodesic structure. <br />
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Joint work with Omer Angel and Gregory Miermont.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120101&date=2018-09-26Number Theory Seminar, Sep 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120249&date=2018-09-26
We will discuss Dieudonné algebras, the de Rham complex, and saturated Dieudonné algebras.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120249&date=2018-09-26Unraveling Controversy on Vexed Environmental Risks, Sep 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120191&date=2018-09-26
Scientific assessment of many contemporary risks is plagued by controversy, persistent uncertainty, and polarized societal contexts. Decision makers often become mired in contested evidence, beset by uncertainties and contradictions. This leads to inaction on early warnings, paralysis-by-analysis, and erodes trust in science and its institutions. But why do controversies persist?<br />
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A new conceptualisation of controversy seeks to unraveling its underlying sources and mechanisms. A new analytical framework maps the interpretive space in scientific assessment stemming from: (1) the multitude of ways in which risk issues can be translated into technical problems (translational diversity); (2) the multitude of tenable styles of scientific reasoning in interpreting evidence (argumentative flexibility) and (3) the existence of deep uncertainty (manufactured and actual) in the science.<br />
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This new framework enables to unravel the interplay of scientific complexity, institutionalized practices of risk appraisal and societal discourses: Societal conflicts and interests co-shape the ways in which evidence is produced, communicated and used and how uncertainty is dealt with, in often hidden ways. Regulatory institutional settings co-define whose evidence counts and what style of scientific reasoning dominates. By integrating perspectives from 4 fields into an interdisciplinary analytical model, the interplay of scientific assessment with its polarised contexts can by analysed more systematically. Examples in the talk will draw on the controversy on neonicotinoids and pesticides.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120191&date=2018-09-26Topology Seminar (Main Talk), Sep 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120312&date=2018-09-26
We study properly convex real projective structures on closed 3-manifolds. A hyperbolic structure is one special example, and in some cases the hyperbolic structure may be deformed non-trivially as a convex projective structure. However, such deformations seem to be exceedingly rare. By contrast, we show that many closed hyperbolic manifolds admit a second convex projective structure not obtained through deformation. We find these examples through a theory of properly convex projective Dehn filling, generalizing Thurston’s picture of hyperbolic Dehn surgery space. Joint work with Sam Ballas, Gye-Seon Lee, and Ludovic Marquis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120312&date=2018-09-26Mathematics Department Colloquium, Sep 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120266&date=2018-09-27
A great deal of fundamental mathematics has been directed at the question of "hearing the shape of a drum," or reading geometric features of a plane domain or manifold off from its Laplace spectrum. I'll address a parallel question in symbolic dynamics: if you have a Euclidean polygon and only know the sequences of sides struck in succession by billiard trajectories—that is, the bounce spectrum—does it determine the polygon? Spoiler: The answer is basically yes. This is joint work with Erlandsson, Leininger, and Sadanand.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120266&date=2018-09-27CANCELED: Student Probability/PDE Seminar, Sep 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120062&date=2018-09-28
It is well-known that diffusions with gradient drifts exhibit metastable behavior. The large deviation estimates of Wentzel-Freidlin and classical Eyring-Kramers Formula give a precise description for such metastable behavior. For non-gradient models, the large-deviation techniques are still applicable, though no rigorous analog of Eyring-Kramers Formula is available. In this talk I give an overview of the existing results and conjectures for general metastable diffusions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120062&date=2018-09-28Logic Colloquium, Sep 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120270&date=2018-09-28
A first order structure is homogeneous if any partial automorphism defined on a finite set extends to an automorphism of the full structure. I will present the first steps towards a classification of homogeneous structures which have few finite substructures. Peter Cameron and Dugald Macpherson conjectured some 30 years ago that such structures are tree-like or order-like. Model-theoretic results on NIP theories can be used to classify the order-like case. Applications include the classification of homogeneous structures in a language consisting of n linear orders and their reducts.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120270&date=2018-09-28Student / postdoc PDE seminar, Sep 28
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120354&date=2018-09-28
We prove in a radially symmetric geometry, the convergence in the sharp interfacial limit, to motion by mean curvature of a second order gradient model for phase transition. This is in spirit similar to the classical Allen-Cahn theory of phase boundary motion. However the corresponding dynamical equation is fourth order thus creating some challenging difficulties for its analysis. A characterization and stability analysis of the optimal profile are performed which are in turn used in the proof of convergence of an asymptotic expansion. (This is joint work with Drew Swartz.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120354&date=2018-09-28Combinatorics Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120268&date=2018-10-01
A cellular string of a polytope is a sequence of faces of the polytope that are stacked on top of each other in a particular direction. The collection of cellular strings, ordered by refinement, forms a poset that is homotopy equivalent to a sphere. Among the set of strings, the subposet of coherent ones is homeomorphic to a sphere. In this talk, I will give an oriented matroid characterization of zonotopes whose poset of cellular strings is a sphere, i.e. for which all strings are coherent. This is based on joint work with Rob Edman, Pakawut Jiradilok, and Gaku Liu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120268&date=2018-10-01String-Math Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120355&date=2018-10-01
Several deep mathematical and physical results such as Kontsevich's deformation-quantization, Drinfeld's associators, and the Deligne hypothesis are controlled by the vanishing of certain obstruction classes in the theory of differential graded operads. I will talk about a way to obtain such vanishing results, as well as higher-genus analogues, using a weight theory implied by a new motivic point of view on the conformal operad.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120355&date=2018-10-01Northern California Symplectic Geometry Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120428&date=2018-10-01
See bulletin board for abstracts.<br />
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Please contact alanw@math.berkeley.edu to request or offer a ride for carpools leaving Evans Hall at 1:15 PM.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120428&date=2018-10-01Differential Geometry Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120228&date=2018-10-01
In the early 80's, Yau conjectured that in any closed $3$-manifold there should be infinitely many minimal surfaces. I will review previous contributions to the question and present a proof of the conjecture, which builds on min-max methods developed by F. C. Marques and A. Neves. A key step is the construction by min-max theory of a sequence of closed minimal surfaces in a manifold N with non-empty stable boundary, and I will explain how to achieve this via the construction of a non-compact cylindrical manifold.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120228&date=2018-10-01Arithmetic Geometry and Number Theory RTG Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120427&date=2018-10-01
Pre-talk: For a Galois representation of a number field arising from a smooth projective variety, the Weil conjecture tells that its Frobenius traces are rational numbers. Fontaine and Mazur conjectured that Galois representations satisfying a local condition (de Rham) arise from geometry and hence have a similar finiteness property of Frobenius traces. In the pretalk, I will explain these backgrounds.<br />
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Main talk: Etale local systems on an algebraic variety are a natural generalization of Galois representations of a filed. In the main talk, I will focus on de Rham local systems and explain a finiteness result on Frobenius traces follows from the Fontaine-Mazur conjecture for Galois representations and the generalized Riemann Hypothesis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120427&date=2018-10-01Analysis and PDE Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120476&date=2018-10-01
The systems of coupled NLS equations occur in some physical problems, in particular in nonlinear optics (coupling between two optical waveguides, pulses or polarized components…). From the mathematical point of view, the coupling effects can lead to truly nonlinear behaviors, such as the beating effect (solutions with Fourier modes exchanging energy) of Grébert, Paturel and Thomann (2013). In this talk, I will use the coupling between two NLS equations on the 1D torus to construct a family of linearly unstable tori, and therefore unstable quasi-periodic solutions. The idea is to take profit of the Hamiltonian structure of the system via the construction of a Birkhoff normal form and the application of a KAM theorem. In particular, we will see of this surprising behavior (this is the first example of unstable tori for a 1D PDE) is strongly related to the existence of beating solutions.<br />
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This is a work in collaboration with Benoît Grébert.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120476&date=2018-10-01Seminar 217, Risk Management: Predicting Portfolio Return Volatility at Median Horizons, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118742&date=2018-10-02
Commercially available factor models provide good predictions of short-horizon (e.g. one day or one week) portfolio volatility, based on estimated portfolio factor loadings and responsive estimates of factor volatility. These predictions are of significant value to certain short-term investors, such as hedge funds. However, they provide limited guidance to long-term investors, such as Defined Benefit pension plans, individual owners of Defined Contribution pension plans, and insurance companies. Because return volatility is variable and mean-reverting, the square root rule for extrapolating short-term volatility predictions to medium-horizon (one year to five years) risk predictions systematically overstates (understates) medium-horizon risk when short-term volatility is high (low). In this paper, we propose a computationally feasible method for extrapolating to medium-horizon risk predictions in one-factor models that substantially outperforms the square root rule.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118742&date=2018-10-02Symplectic Working Group, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120543&date=2018-10-02
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120543&date=2018-10-023-Manifold Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120475&date=2018-10-02
We'll continue to discuss Thaddeus' proof that the trace of a simple closed curve is a perfect Morse function on the projective SU(2) representation variety of a surface.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120475&date=2018-10-02Probabilistic Operator Algebra Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119984&date=2018-10-02
One may think of an "independence relation" as a prescription for building joint distributions of (non-commutative) random variables, satisfying some nice universality properties. Work of Muraki and of Ben Ghorbal and Schurmann has shown that there are very few such universal independences; even with the fewest required "nice properties", there are no more than five. In this talk I will give an introduction to monotonic independence of random variables which fits in only the broadest category as it is not symmetric: $X$ being monotonically independent from $Y$ is \emph {not} equivalent to $Y$ being monotonically independent from $X$. Our goal will be to investigate the behaviour of additive monotonic convolution: given probability measures µ and ν, and random variables $X \sim \mu $ and $Y \sim \nu $ in some algebra where $X$ is monotonically indepenedent from $Y$, what is the distribution of $X+Y$? I will cover the analytic techniques necessary to answer this question, and in the time remaining, begin an investigation into monotone infinite divisibility and semigroups of convolution. This talk will draw material variously from papers of Muraki, of Bercovici and of Hasebe.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119984&date=2018-10-02The challenge of big data and data science for the social sciences, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120009&date=2018-10-02
The 2005 National Science Foundation workshop report on "Cyberinfrastructure for the Social and Behavioral Sciences" (Fran Berman and Henry Brady) argued that the methods of doing research in the social sciences would be transformed by big data and data science and that the social sciences should be centrally involved in studying the impacts of big data and data science on society. In "The Challenge of Big Data and Data Science," just completed for the Annual Review of Political Science, I have brought these arguments up-to-date. I will talk about defining "big data" and "data science," about the new kinds of research being done in the social sciences over the past decade that use big data and data science methods, and about the impacts of the information revolution on warfare, cities, the media, health care, and jobs and the ways that the social sciences must come to grips with them.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120009&date=2018-10-02Topology Seminar (Introductory Talk), Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120544&date=2018-10-03
In this introductory talk, we will discuss periodic dynamics on (punctured ) 2-torus, its algebraic incarnations, and its relations to dynamics on elliptic curves. In particular, we will give a geometric picture of how this could be used to distinguish total spaces of fibrations over tori/of analytic fibrations over elliptic curves. We will also try to demonstrate the periodic behavior of "flow lines" can survive in degenerate cases at an algebraic level.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120544&date=2018-10-03Concentration from Geometry in High Dimension, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120103&date=2018-10-03
The concentration of Lipschitz functions around their expectation is a classical topic that continues to be very active. We will discuss some recent progress, including: <br />
1- A tight log-Sobolev inequality for isotropic logconcave densities<br />
2- A unified and improved large deviation inequality for convex bodies<br />
3- An extension of the above to Lipschitz functions (generalizing the Euclidean squared distance)<br />
The main technique of proof is a simple iteration (equivalently, a Martingale process) that gradually transforms any density into one with a Gaussian factor, for which isoperimetric inequalities are considerably easier to establish. The talk is joint work with Yin Tat Lee (UW) and will involve some elementary calculus.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120103&date=2018-10-03Number Theory Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120426&date=2018-10-03
We will discuss the construction of $W\Omega _R^\ast $ and the comparison with the de Rham complex.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120426&date=2018-10-03Topology Seminar (Main Talk), Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120425&date=2018-10-03
One can construct the open symplectic mapping torus \(T_\phi \) for a given a Weinstein manifold \(M\) and a compactly supported symplectomorphism \(\phi \). Its contact boundary is independent of \(\phi \) and is equal to contact boundary of \(T_0\times M\) where \(T_0\) is the torus with a small ball removed. In this talk, we will outline a method to distinguish the fillings \(T_\phi \) and \(T_0\times M\). We will exploit the dynamics and deformation theory of the (wrapped) Fukaya categories, where the dynamics of the same sort is invisible at a geometric level.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120425&date=2018-10-03Statistical challenges in casualty estimation, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120434&date=2018-10-03
An accurate understanding of the magnitude and dynamics of casualties during a conflict is important for a variety of reasons, including historical memory, retrospective policy analysis, and assigning culpability for human rights violations. However, during times of conflict and their aftermath, collecting a complete or representative sample of casualties can be difficult if not impossible. One solution is to apply population estimation methods-- sometimes called capture-recapture or multiple systems estimation-- to multiple incomplete lists of casualties to estimate the number of deaths not recorded on any of the lists. In this talk, I give an introduction to the procedures by which population estimation is performed in the context of conflict mortality, which mainly consists of a record linkage step followed by capture-recapture estimation. I then describe some of my recent work in this area, which is directed at elucidating the limitations of these statistical methods and proposing variants with better properties. I will conclude with a discussion of open questions in this challenging area of applied statistics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120434&date=2018-10-03Representation Theory and Mathematical Physics Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120542&date=2018-10-03
We propose a categorification of link invariants in Euclidean 3d space associated to a semi-simple Lie algebra, based on category of A-branes in finite dimensional Landau-Ginzburg (LG) models. The category of A-branes in such abstract LG model was constructed recently by Gaiotto, Moore and Witten; its mathematical counterpart is a version of Fukaya-Seidel category. The specific Landau-Ginzburg model needed is derived from string theory. We explain the relation to some other approaches to the same problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120542&date=2018-10-03Center for Computational Biology Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120220&date=2018-10-03
Title: Making sense of the “noise” in cancer data<br />
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During carcinogenesis, cells accumulate 1000s of somatic DNA mutations. “Driver” mutations bestow fitness advantages that lead to selective sweeps that increase that frequency of mutated cells compared to those lacking the driver. These sweeps also increase the frequency of “passenger” mutations accumulated since the last such sweep. These mutations have little impact on cell function but provide information about the mutational processes that generated them. Both their type (i.e., A to C) and genomic locations depend not only what caused the mutation -- e.g., UV light – but also the chromatin state of the cell that acquired it. My lab developed Bayesian inference methods to classify somatic mutations into different ‘subclones’ that correspond to different sweeps. Our methods also use phylogenetic approaches to determine the relative order in which the sweeps occurred. We are now developing supervised and unsupervised learning methods to interpret this historical record of the cancer, in order to use the timing and patterns of somatic mutations to reconstruct the changes that a normal cell underwent during its transformation into a cancerous cell.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120220&date=2018-10-03Applied Math Seminar, Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120145&date=2018-10-04
In this talk, I begin wtih the nonlinear Schroedinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, quantum physics and chemistry, etc., and review some dynamical properties of NLSE/GPE including conserved quantities, dispersion relation, center-of-mass dynamics, soliton solutions and semiclassical limits. Different numerical methods will be presented including finite different time domain (FDTD) methods and time-splitting spectral method, and their error estimates and comparison will be discussed. Extensions to NLSE/GPE with an angular momentum rotation term and/or non-local dipole-dipole interaction as well as multi-component will be presented. Finally, applications to soliton interactions, collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120145&date=2018-10-04Student Probability/PDE Seminar, Oct 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120267&date=2018-10-05
It is well-known that diffusions with gradient drifts exhibit metastable behavior. The large deviation estimates of Wentzel-Freidlin and classical Eyring-Kramers Formula give a precise description for such metastable behavior. For non-gradient models, the large-deviation techniques are still applicable, though no rigorous analog of Eyring-Kramers Formula is available. In this talk I give an overview of the existing results and conjectures for general metastable diffusions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120267&date=2018-10-05Combinatorics Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119664&date=2018-10-08
We study the Taylor expansion around the point $x=1$ of a classical modular form, the Jacobi theta constant $\theta_3$. This leads naturally to a new sequence $(d(n))^\infty_{n=0} =1,1,−1,51,849,−26199,\dots$ of integers, which arise as the Taylor coefficients in the expansion of a related "centered" version of $\theta_3$. We prove several results about the numbers $d(n)$ and conjecture that they satisfy the congruence $d(n)\cong (−1)^{n−1} (mod\, 5)$ and other similar congruence relations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119664&date=2018-10-08String-Math Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120356&date=2018-10-08
A conjecture of Dunfield-Gukov-Rasmussen predicts a family of differentials on reduced HOMFLY-PT homology, indexed by the integers, that give rise to a corresponding family of reduced link homologies. We'll discuss a variant of this conjecture, constructing an unreduced link homology theory categorifying the quantum \(gl_n\) link invariant for all non-zero values of \(n\) (including negative values!). To do so, we employ the technique of annular evaluation, which uses categorical traces to define and characterize type A link homology theories in terms of simple data assigned to the unknot. Of particular interest is the case of negative n, which gives a categorification of the "symmetric webs" presentation of the type A Reshetikhin-Turaev invariant, and which produces novel categorifications thereof (i.e. distinct from the Khovanov-Rozansky theory).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120356&date=2018-10-08Differential Geometry Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120313&date=2018-10-08
We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\mbox {PIC}_1$ cases, of which the results are new. We complete the discussion of the almost preservation problem by Bamler-Cabezas-Rivas-Wilking, and the 2-non-negative case generalizes a result in 3D by Simon-Topping to higher dimensions. As an application, we use the local Ricci flow to smooth a metric space which is the limit of a sequence of manifolds with the almost non-negative curvature conditions, and show that this limit space is bi-Hölder homeomorphic to a smooth manifold.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120313&date=2018-10-08Arithmetic Geometry and Number Theory RTG Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120674&date=2018-10-08
There is a canonical pairing on the Brauer group of a surface over a ﬁnite ﬁeld, and an old conjecture of Tate predicts that this pairing is alternating. In this talk I will present a resolution to Tate’s conjecture. The key new ingredient is a circle of ideas originating in algebraic topology, centered around the Steenrod operations. The talk will advertise these new tools (while assuming minimal background in algebraic topology).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120674&date=2018-10-08Seminar 217, Risk Management: Robust Learning: Information Theory and Algorithms, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118749&date=2018-10-09
This talk will provide an overview of recent results in high-dimensional robust estimation. The key question is the following: given a dataset, some fraction of which consists of arbitrary outliers, what can be learned about the non-outlying points? This is a classical question going back at least to Tukey (1960). However, this question has recently received renewed interest for a combination of reasons. First, many of the older results do not give meaningful error bounds in high dimensions (for instance, the error often includes an implicit sqrt(d)-factor in d dimensions). Second, recent connections have been established between robust estimation and other problems such as clustering and learning of stochastic block models. Currently, the best known results for clustering mixtures of Gaussians are via these robust estimation techniques. Finally, high-dimensional biological datasets with structured outliers such as batch effects, together with security concerns for machine learning systems, motivate the study of robustness to worst-case outliers from an applied direction.<br />
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The talk will cover both information-theoretic and algorithmic techniques in robust estimation, aiming to give an accessible introduction. We will start by reviewing the 1-dimensional case, and show that many natural estimators break down in higher dimensions. Then we will give a simple argument that robust estimation is information-theoretically possible. Finally, we will show that under stronger assumptions we can perform robust estimation efficiently, via a "dual coupling" inequality that is reminiscent of matrix concentration inequalities.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118749&date=2018-10-09Symplectic Working Group, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120632&date=2018-10-09
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120632&date=2018-10-09Probabilistic Operator Algebra Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120726&date=2018-10-09
The lattice of non-crossing partitions plays a crucial role in free probability, giving rise to the free cumulants introduced by Roland Speicher. In addition to their combinatorial description, the non-crossing partitions can be realized as arising from the Coxeter groups of Type A. Reiner used this analogy to introduce the non-crossing partitions of Type B, which raises the question: what do these correspond to on the non-commutative probability side ? It turns out that the Type B theory leads to a kind of infinitesimal free independence. In this expository talk, we will present these ideas and discuss (briefly) how they can be applied to understand finite rank perturbations of random matrices.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120726&date=2018-10-09Letters of recommendation in Berkeley undergraduate admissions: Program evaluation and natural language processing, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120051&date=2018-10-09
In Fall 2015 and 2016, UC Berkeley asked many freshman applicants to submit letters of recommendation as part of their applications. This was highly controversial. Proponents argued that letters would aid in the identification of disadvantaged students who had overcome obstacles that were not otherwise apparent from their applications, while opponents argued that disadvantaged students were unlikely to have access to adults who could write strong letters. I oversaw an experiment in the 2016-17 admissions cycle in which applications were scored with and without their letters. Initial analysis of the experiment indicated that when available the letters modestly improved the reader scores of students from underrepresented groups, and that few otherwise admissible students failed to submit letters when asked. I will also present results of a textual analysis of the letters themselves, using natural language processing to measure differences in the letters that underrepresented students receive compared to otherwise similarly qualified students not from underrepresented groups.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120051&date=2018-10-09Topology Seminar (Introductory Talk), Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120677&date=2018-10-10
Starting with closed symplectic manifolds, we introduce Hamiltonian Floer homology and discuss the dynamical information it encodes. We then translate this story to open symplectic manifolds, on which symplectic cohomology is defined.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120677&date=2018-10-10Bay Area Microlocal Analysis Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120503&date=2018-10-10
We study the trapped set of spacetimes whose metric decays to a stationary Kerr metric at an inverse polynomial rate. In the first part of the talk, I will focus on the dynamical aspects of this problem and show that the trapped set is a smooth submanifold which converges to that of the stationary metric at the same rate. In the second part, I will explain how to use this to prove microlocal estimates at the trapped set for solutions of wave equations on such spacetimes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120503&date=2018-10-10Large deviations of subgraph counts for sparse Erd\H{o}s--R\'enyi graphs, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120664&date=2018-10-10
For each fixed integer $\ell\ge 3$ we establish the leading order of the exponential rate function for the probability that the number of cycles of length $\ell$ in the Erd\H{o}s--R\'enyi graph $G(N,p)$ exceeds its expectation by a constant factor, assuming $N^{-1/2}\ll p\ll 1$ (up to log corrections) when $\ell\ge 4$, and $N^{-1/3}\ll p\ll 1$ in the case of triangles. We additionally obtain the upper tail for general subgraph counts, as well as the lower tail for counts of seminorming graphs, in narrower ranges of sparsity. As in other recent works on the emerging theory of nonlinear large deviations, our general approach applies to functions on product spaces which are of ``low complexity", though the notion of complexity used here is somewhat different. Based on joint work with Amir Dembo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120664&date=2018-10-10Number Theory Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120633&date=2018-10-10
We will discuss the classical de Rham Witt complex and Zariski localization.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120633&date=2018-10-10To persist or not to persist?, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120151&date=2018-10-10
Two long standing, fundamental questions in biology are "Under what conditions do populations persist or go extinct? When do interacting species coexist?" The answers to these questions are essential for guiding conservation efforts and identifying mechanisms that maintain biodiversity. Mathematical models play an important role in identifying these mechanisms and, when coupled with empirical work, can determine whether or not a given mechanism is operating in a specific population or community. For over a century, nonlinear difference and differential equations have been used to identify these mechanisms. These models, however, fail to account for stochastic fluctuations in environmental conditions such as temperature and precipitation. In this talk, I present theorems about persistence, coexistence, and extinction for stochastic difference equations that account for species interactions, population structure, and environmental fluctuations. The theorems will be illustrated with models of Bay checkerspot butterflies, spatially structured acorn woodpecker populations, competition among Kansas prairie grass species, and the evolutionary game of rock, paper, and scissors. This work is in collaboration with Michel Benaim.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120151&date=2018-10-10Bay Area Microlocal Analysis Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120504&date=2018-10-10
I will show a frequency-independent lower bound on mass of eigenfunctions on surfaces of variable negative curvature. This was previously done in the case of constant curvature in joint work with Jin, relying on the fractal uncertainty principle proved in joint work with Bourgain. I will focus on the new components needed to handle the case of variable curvature, in particular propagation of quantum observables up to local Ehrenfest time. Joint work in progress with Long Jin and Stéphane Nonnenmacher.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120504&date=2018-10-10Topology Seminar (Main Talk), Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120678&date=2018-10-10
Mirror symmetry predicts the existence of Floer invariants that yield “local” information. Guided by this, we construct a quantitative symplectic cohomology theory that detects Floer-essential Lagrangians within subdomains. We illustrate the quantitative behavior of this theory by examining negative line bundles over toric symplectic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120678&date=2018-10-10Applied Math Seminar, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119846&date=2018-10-11
This talk will address the issue of closure in reduced order models (ROMs) and large eddy simulations (LES), leveraging ideas from non-equilibrium statistical mechanics. The approach is based on the Variational Multi-Scale method (VMS) and the Mori-Zwanzig (M-Z) formalism, which provides a framework to perform formal scale separation and re-cast a high-dimensional dynamical system into an equivalent, lower-dimensional system. In this reduced system, which is in the form of a generalized Langevin equation (GLE), the effect of the unresolved modes on the resolved modes appears as a convolution integral (which is sometimes referred to as memory). The M-Z formalism alone does not lead to a reduction in computational complexity as it requires the solution of the orthogonal dynamics PDE. A model for the memory is constructed by assuming that memory effects have a finite temporal support and by exploiting scale similarity. We discover that unresolved scales lead to memory effects that are driven by an orthogonal projection of the coarse-scale residual and inter-element jumps (in the case of discontinuous finite elements). It is further shown that an MZ-based finite memory model is a variant of the well-known adjoint-stabilization method. For hyperbolic equations, this stabilization is shown to have the form of an artificial viscosity term. We further establish connections between the memory kernel and approximate Riemann solvers. In the context of ROMs, this model is shown to yield a Petrov-Galerkin projection. Several applications in ROMs and LES ranging from simple scalar PDEs to Magneto-hydro-dynamic turbulence will be presented.<br />
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Bio: Karthik Duraisamy is an Associate Professor of Aerospace Engineering at the University of Michigan, Ann Arbor. He obtained a doctorate in aerospace engineering and masters in applied mathematics from the University of Maryland, College Park. He is the director of the Center for Data-driven Computational Physics and the associate director of the Michigan Institute of Computational Discovery and Engineering (MICDE) at the Univ of Michigan. His research interests are in data-driven and reduced order modeling, turbulence modeling and simulations, and numerical methods for PDEs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119846&date=2018-10-11Mathematics Department Colloquium, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120272&date=2018-10-11
(joint with B.Bakker and Y.Brunebarbe) One very fruitful way of studying complex algebraic varieties is by forgetting the underlying algebraic structure, and just thinking of them as complex analytic spaces. To this end, it is a natural and fruitful question to ask how much the complex analytic structure remembers. One very prominent result is Chows theorem, stating that any closed analytic subspace of projective space is in fact algebraic. One notable consequence of this result is that a compact complex analytic space admits at most 1 algebraic structure - a result which is false in the non-compact case. This was generalized and extended by Serre in his famous GAGA paper using the language of cohomology.<br />
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We explain how we can extend Chow's theorem and in fact all of GAGA to the non-compact case by working with complex analytic structures that are "tame" in the precise sense defined by o-minimality. This leads to some very general "algebraization" theorems, and we give applications to Hodge theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120272&date=2018-10-11Student Probability/PDE Seminar, Oct 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120673&date=2018-10-12
We shall first recall how to obtain macroscopic PDEs by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. We shall then construct along these lines explicit examples of spontaneous energy generation (and therefore establish non-uniqueness) for the compressible Euler system, with and without pressure. The examples come from rescalings of well-posed deterministic systems of molecules that either collide elastically or interact via singular pair potentials. They live in space dimension 1 for the Euler with pressure and in higher dimensions, but have singular support, for the pressureless Euler. (Work with Jianfei Xue.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120673&date=2018-10-12Logic Colloquium, Oct 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120271&date=2018-10-12
One of the goals of proof theory is to find combinatorial characterization of sentences provable in particular theories, i.e., to present these sentences as mathematical principles, rather than mere syntactical statements. While for strong theories these sentences tend to be incomprehensible, for weak theories we expect to find something familiar, or at least similar to well-known principles. In this talk I will report on the project to characterize provably disjoint NP pairs of sets in systems called Bounded depth Frege systems. The resulting characterization is expressed in terms of positional strategies in some combinatorial games that generalize the standard concept of a finite game.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120271&date=2018-10-12Combinatorics Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120269&date=2018-10-15
Many questions in combinatorics, probability and statistical mechanics can be reduced to counting lattice paths (walks) in regions of the plane. A standard approach to counting problems is to consider properties of the associated generating function. These functions have long been well understood for walks in the full plane and in a half plane. Recently much attention has focused on walks in the first quadrant of the plane and has now resulted in a complete characterization of those walks whose generating functions are algebraic, holonomic (solutions of linear differential equations) or at least differentially algebraic (solutions of algebraic differential equations). I will give an introduction to this topic, discuss previous work of Bousquet-Melou, Kauers, Mishna, and others and then present recent work by Dreyfus, Hardouin, Roques and myself applying the theory of QRT maps and Galois theory of difference equations to determine which generating functions satisfy differential equations and which do not.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120269&date=2018-10-15String-Math Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120725&date=2018-10-15
A conjecture of Gorsky-Negut-Rasmussen asserts the existence of a pair of adjoint functors relating the Hecke category for symmetric groups and the Hilbert scheme of points in the plane. One topological consequence of this conjecture is the prediction of a deformation of the triply graded Khovanov-Rozansky link homology which restores the missing \(q\rightarrow tq^{-1}\) symmetry of KR homology for links. In this talk I will discuss a candidate for such a deformation, constructed in joint work with Eugene Gorsky, which indeed facilitates connections with Hilbert schemes. For instance our main result explicitly computes the homologies (both deformed and undeformed) of the \((n,nk)\) torus links, summed over all \(n\geq 0\), as a graded algebra. Combining with work of Haiman this gives a functor from the Hecke category to sheaves on the relevant Hilbert scheme.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120725&date=2018-10-15Differential Geometry Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120505&date=2018-10-15
This is joint work with M. Eichmair and V. Moraru. We prove that if a 3-manifold with non-negative scalar curvature contains an absolutely area-minimizing cylinder then the ambient manifold is flat. This can be seen as a scalar curvature analogue of the Cheeger–Gromoll splitting theorem for Ricci curvature.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120505&date=2018-10-15Arithmetic Geometry and Number Theory RTG Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120840&date=2018-10-15
The local (and global) Langlands conjectures attempt to bridge the major areas of harmonic analysis and number theory by forming a correspondence between representations which naturally appear in both areas. A key insight due to Langlands and Kottwitz is that one could attempt to understand such a conjectural correspondence by comparing the traces of natural operators on both sides of the bridge. Moreover, it was realized that Shimura varieties present a natural means of doing this. For global applications, questions of reduction type (at a particular prime $p$) for these Shimura varieties can often be avoided, and for this reason the methods of Langlands and Kottwitz focused largely on the setting of good reduction. But, for local applications dealing with the case of bad reduction is key. The setting of bad reduction was first dealt with, for some simple Shimura varieties. Harris and Taylor then used this, together with the work of many other mathematicians, to prove the local Langlands conjecture for $GL_n$. A decade later Scholze gave an alternative, more geometric, way to understand the case of bad reduction for certain Shimura varieties and was able to reprove the local Langlands conjecture for $GL_n$ in simpler terms. In this talk we will discuss an extension of the ideas of Scholze to a wider class of Shimura varieties, as well as the intended application of these ideas to the local Langlands conjectures for more general groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120840&date=2018-10-15Analysis and PDE Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120836&date=2018-10-15
In this talk, I will discuss the differential equation $iu_t = Hu, H := H_0 + V$ , where $V$ is a decaying potential and $H_0$ is a Laplacian related operator. In particular, I will focus on when $H_0$ is Laplacian, Bilaplacian and Dirac operators. I will discuss how the threshold energy obstructions, eigenvalues and resonances, effect the $L^1 \to L^\infty $ behavior of $e^{itH} P_{ac} (H)$. The threshold obstructions are known as the distributional solutions of $H\psi = 0$ in certain dimension dependent spaces. Due to its unwanted effects on the dispersive estimates, its absence have been assumed in many work. I will mention our previous results on Dirac operator and recent results on Bilaplacian operator under different assumptions on threshold energy obstructions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120836&date=2018-10-15Deformation Theory Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120824&date=2018-10-15
Let $A$ be an algebra. The Koszul duality is a type of derived equivalence between modules over $A$ and modules over its Koszul dual $A^!$. In this talk, we will talk about the general framework and then focus on the classical cases as well as examples.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120824&date=2018-10-15Representation theory seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120838&date=2018-10-16
Khovanov and Rozansky defined a link invariant called triply graded homology. It is conjectured by Gorsky, Negut and Rasmussen that this invariant can be expressed geometrically by a functor from complexes of Soergel bimodules to the derived category of coherent sheaves on the dg flag Hilbert scheme followed by taking cohomology. A functor with similar properties has been constructed by Oblomkov and Rozansky using matrix factorizations and it is believed that this functor solves the conjecture. The aim of this joint work in progress with Roman Bezrukavnikov is to relate the two constructions using previous work of Arkhipov and Kanstrup.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120838&date=2018-10-16Seminar 217, Risk Management: Asymptotic Spectral Analysis of Markov Chains with Rare Transitions: A Graph-Algorithmic Approach, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118748&date=2018-10-16
Parameter-dependent Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. Such processes often manifest metastability, and the spectral properties of the generators largely govern their long-term dynamics. In this work, we propose a constructive graph-algorithmic approach to computing the asymptotic estimates of eigenvalues and eigenvectors of the generator. In particular, we introduce the concepts of the hierarchy of Typical Transition Graphs and the associated sequence of Characteristic Timescales. Typical Transition Graphs can be viewed as a unification of Wentzell’s hierarchy of optimal W-graphs and Friedlin’s hierarchy of Markov chains, and they are capable of describing typical escapes from metastable classes as well as cyclic behaviors within metastable classes, for both reversible and irreversible processes. We apply the proposed approach to conduct zero-temperature asymptotic analysis of the stochastic network representing the energy landscape of the Lennard-Jones cluster of 75 atoms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118748&date=2018-10-163-Manifold Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120839&date=2018-10-16
Bass-Serre theory studies groups acting on trees. The action of a group on a tree determines a quotient "graph of groups", from which one can reconstruct the original group via amalgamated free products and HNN extensions. We will study the tree associated to $PSL(2,{\mathbb Q}_p)$ in detail, discuss various higher-dimensional generalizations, and describe some applications to the study of incompressible surfaces in 3-manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120839&date=2018-10-16Student Harmonic Analysis and PDE Seminar (HADES), Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120842&date=2018-10-16
I will present the method introduced by András Vasy to prove meromorphic continuations of resolvents of Laplacians on asymptotically hyperbolic spaces in a simple model case. In particular, I will show the proof of Melrose's radial estimates indicating the idea behind the general case.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120842&date=2018-10-16Probabilistic Operator Algebra Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120579&date=2018-10-16
With the introduction of free independence by D.V. Voiculescu, it became clear that in the framework of non-commutative probability there are other notions of independence than that of classical independence. The Boolean convolution between measures was formally introduced by Speicher and R. Woroudi in 1993, although it had previously appeared in the literature in different contexts, for example, as partial cumulants in stochastic differential equations. Later, in 2006, H. Bercovici provided the product for Hilbert spaces that, in the context of operator algebras, corresponds to the Boolean convolution between measures. In this talk we will survey the basics of Boolean probability, scenarios in which it appears naturally, together with some results that show the similarities and differences it has with the classical theory of probability.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120579&date=2018-10-16Topology Seminar (Introductory Talk), Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120679&date=2018-10-17
Random curves in space and how they are knotted give an insight into the behavior of "typical" knots and links. They have been studied by biologists and physicists in the context of the structure of random polymers. Several randomized models have been suggested and investigated both by theoretical methods and computational experiments. We will review some known and new models of random knotting, and will discuss their nature and the typical properties of the knots they produce.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120679&date=2018-10-17The Lovász theta function for random regular graphs, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120791&date=2018-10-17
The Lovász theta function is a classic semidefinite relaxation of graph coloring. In this talk I'll discuss the power of this relaxation for refuting colorability of uniformly random degree-regular graphs, as well as for distinguishing this distribution from one with a `planted' disassoratative community structure. We will see that the behavior of this refutation scheme is consistent with the conjecture that coloring and community detection exhibit a `computationally hard but information-theoretically feasible' regime typical of random constraint satisfaction and statistical inference problems. The proofs will make use of orthogonal polynomials, nonbacktracking walks, and results on the spectra of random regular graphs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120791&date=2018-10-17Number Theory Seminar, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120727&date=2018-10-17
We will discuss étale localization in the theory of the de Rham Witt complex.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120727&date=2018-10-17Topology Seminar (Main Talk), Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120680&date=2018-10-17
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and arises also in applications to the natural sciences. We will discuss knots that arise from random permutations using petal projections (Adams et al. 2012). We will explain why the probability of obtaining any given knot type in this model is positive if the number of petals is at least linear in the knot's crossing number, and why it decays to zero as this number grows to infinity. Our approach uses different knot invariants and arguments than those that have been used in other random models.<br />
<br />
Joint work with Joel Hass, Nati Linial, and Tahl Nowik.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120680&date=2018-10-17Learning in Google Ads, Machines and People, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120789&date=2018-10-17
This talk is in two parts, both of which discuss interesting uses of experiments in Google search ads. In part 1 I discuss how we can inject randomness into our system to get causal inference in a machine learning setting. In part 2. I talk about experiment designs to measure how users learn in response to ads on Google.com.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120789&date=2018-10-17Applied Math Seminar, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120675&date=2018-10-18
Electronic correlation effects play an import role in emergent phenomena such as Mott-insulator-metal transition and unconventional superconductivity. Understanding these effects present a theoretical challenge. In this talk, we will give an overview of dynamical mean-field theory (DMFT) and its combination with the local density approximation in density functional theory. Representative quantum impurity solvers including continuous-time quantum Monte Carlo method will also be discussed, together with a few measurable quantities. Finally, I will present applications of the theoretical approach to strongly correlated f-electron systems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120675&date=2018-10-18Mathematics Department Colloquium, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120841&date=2018-10-18
This is a joint work with Piermarco Cannarsa and Wei Cheng. <br />
<br />
If A is a closed subset of the Euclidean space $R^k$, the Euclidean distance function $d_A : R^k \to [0, + \infty[$ is defined by<br />
<br />
$$d_A(x) = \mathrm{min}_{a \in A} ||x − a||.$$<br />
<br />
This function is Lipschitz, therefore differentiable almost everywhere. We will give topological properties of the set Sing(F) of points in $R^k \setminus M$ where F is not differentiable. For example it is locally connected. We will also discuss the homotopy type of Sing(F).<br />
<br />
Although, we will concentrate on $d_A$, we will explain that it is a particular case of a more general result on the singularities of a viscosity solution $F:R^k × ]0, +\infty[ \to R$ of the evolution Hamilton-Jacobi equation<br />
<br />
$$ \partial_t F + H(x, \partial_x F) = 0,$$<br />
<br />
where $H : R^k × R^k \to R$, $(x, p) \mapsto H(x, p)$ is a $C^2$ Tonelli Hamiltonian, i.e. convex and superlinear in the momentum p. If time permits we will explain the methods of proof for the case of $d_A$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120841&date=2018-10-184th Annual CDAR Symposium 2018, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119719&date=2018-10-19
The fourth annual CDAR Symposium, presented in partnership with State Street, will convene on Friday, October 19, 2018, from 8:30 am to 6:30 pm at UC Berkeley’s Memorial Stadium. Our conference will feature new developments in data science, highlighting applications to finance and risk management. Confirmed speakers include Jeff Bohn, Olivier Ledoit, Ulrike Malmendier, Steven Kou, Ezra Nahum, Roy Henriksson, and Ken Kroner.<br />
<br />
The Consortium for Data Analytics in Risk (CDAR) supports research into innovation in data science and its applications to portfolio management and investment risk. Based in the Economics and Statistics Departments at UC Berkeley, CDAR was co-founded with State Street, Stanford, Berkeley Institute for Data Science (BIDS), and Southwestern University of Finance and Economics (SWUFE). This year, CDAR welcomes a new founding member, Swiss Re based in Switzerland, and a new industry partner, AXA Rosenberg. CDAR organizes conferences, workshops, and research programs, bringing together academic researchers from the physical and social sciences, and industry researchers from financial management firms and technology development companies large and small.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119719&date=2018-10-19Student Probability/PDE Seminar, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120837&date=2018-10-19
We shall first recall how to obtain macroscopic PDEs by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. We shall then construct along these lines explicit examples of spontaneous energy generation (and therefore establish non-uniqueness) for the compressible Euler system, with and without pressure. The examples come from rescalings of well-posed deterministic systems of molecules that either collide elastically or interact via singular pair potentials. They live in space dimension 1 for the Euler with pressure and in higher dimensions, but have singular support, for the pressureless Euler. (Work with Jianfei Xue.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120837&date=2018-10-19Combinatorics Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120823&date=2018-10-22
A Hopf monoid is an algebraic structure that many families of combinatorial objects share. The collection of multiplicative functions defined on a Hopf monoid forms a group, called the character group. Aguiar and Ardila (2017) proved that the character groups for the Hopf monoids of permutahedra and associahedra are exponential power series under multiplication and composition, respectively. In this talk I will introduce the Hopf monoid of orbit polytopes, and then I will discuss some of my recent work on determining the structure of the character group of this Hopf monoid.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120823&date=2018-10-22Differential Geometry Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120724&date=2018-10-22
The notion of a harmonic Z/2 spinor was introduced by Taubes as an abstraction of various limiting objects appearing in compactifications of gauge-theoretic moduli spaces. I will explain this notion and discuss an existence result for harmonic Z/2 spinors on three-manifolds. The proof uses a wall-crossing formula for solutions of generalized Seiberg-Witten equations in dimension three, a result itself motivated by Yang-Mills theory on Riemannian manifolds with special holonomy $G_2$. The talk is based on joint work with Thomas Walpuski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120724&date=2018-10-22Mathematical Theories of Communication: Old and New, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120115&date=2018-10-22
Reliable and efficient digital communication is possible today largely due to some wonderful successes in mathematical modelling and analysis. A legendary figure in this space is Claude Shannon (1916-2001) who laid out the mathematical foundations of communication in his seminal 1948 treatise, where among other contributions he gave a mathematical definition of "entropy" and coined the now ubiquitous term "bit" (for binary digit). But Shannon's theory is not the last word in communication. Communication extends to settings well beyond the carefully designed full information exchange model explored in Shannon's work. In this talk I will try to describe some of the many extensions that have been explored in the interim period including communication complexity (Yao 1980) that explores how it might be possible to achieve effective communication without a full exchange; interactive communication (Schulman 1992) which explores how to cope with errors in an interactive setting, and some of our own work on uncertain communication, which explores how shared context can make communication more effective, even if the context is shared only loosely.<br />
<br />
Light refreshments will be served before the lecture at 3:30 p.m.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120115&date=2018-10-22Seminar 217, Risk Management: Proliferation of Anomalies and Zoo of Factors – What does the Hansen–Jagannathan Distance Tell Us?, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118743&date=2018-10-23
Recent research finds that prominent asset pricing models have mixed success in evaluating the cross-section of anomalies, which highlights proliferation of anomalies and zoo of factors. In this paper, I investigate that how is the relative pricing performance of these models to explain anomalies, when comparing their misspecification errors– the Hansen–Jagannathan (HJ) distance measure. I find that a traded-factor model dominates others in a specific anomaly by incorporating the multiple HJ distance comparing inference. However, different from the current research of Barillas and Shanken (2017) and Barillas, Kan, Robotti and Shanken (2018), I result that the HJ distance is a general statistic measure to compare models and some model-derived non-traded factors even outperform traded factors. Second, there is a large variation in the shape and curvature of these confidence sets of anomalies, which makes any single SDF difficult to satisfy confidence sets of anomalies all. My results imply that further work is required not only in pruning the number of priced factors but also in building models that explain the anomalies better.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118743&date=2018-10-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119669&date=2018-10-23
The uniform probability measure on a convex polytope induces piecewise polynomial densities on the projections of that polytope. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex coordinates. We study projective varieties that are parametrized by finite collections of such rational functions. Our focus lies on determining the prime ideals of these moment varieties. Special cases include Hankel determinantal ideals for polytopal splines on line segments, and the relations among multisymmetric functions given by the cumulants of a simplex. In general, our moment varieties are more complicated, and they offer nice challenges for both numerical and symbolic computing in algebraic geometry. This is joint work with Kathlen Kohn and Boris Shapiro.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119669&date=2018-10-23Probabilistic Operator Algebra Seminar, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120169&date=2018-10-23
In this talk, I will introduce a class of independence relations which include free, Boolean and monotone independence in operator valued probability. I will briefly review some analytic properties of operator-valued free, Boolean and monotone convolutions. After that, I will show some analytic properties of two other important convolutions which are called orthogonal convolution and s-free convolution ( or say subordination convolution). We will see that most convolutions in our framework can be constructed from the orthogonal and the Boolean convolution whereas the s-free convolution is a powerful tool for studying the free additive convolution. Then I will show how to use matricial functions which are derived from Voiculescu's fully matricial function theory, to study relations between convolutions and transforms in operator-valued free probability. If time permits, I will simply explain how to compute large N laws of random matrices with entries of our new independent relations, and we will see that the large N laws are not always semicircular.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120169&date=2018-10-23Optimal robot action for and around people, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120052&date=2018-10-23
Estimation, planning, control, and learning are giving us robots that can generate good behavior given a specified objective and set of constraints. What I care about is how humans enter this behavior generation picture, and study two complementary challenges: 1) how to optimize behavior when the robot is not acting in isolation, but needs to coordinate or collaborate with people; and 2) what to optimize in order to get the behavior we want. My work has traditionally focused on the former, but more recently I have been casting the latter as a human-robot collaboration problem as well (where the human is the end-user, or even the robotics engineer building the system). Treating it as such has enabled us to use robot actions to gain information; to account for human pedagogic behavior; and to exchange information between the human and the robot via a plethora of communication channels, from external forces that the person physically applies to the robot, to comparison queries, to defining a proxy objective function.<br />
<br />
The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120052&date=2018-10-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120578&date=2018-10-23
Given a polynomial ring $C$ over a field and proper ideals $I$ and $J$ whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of $I+J$ into a collection of primes described in terms of the associated primes of select powers of $I$ and of $J$. We discuss applications to constructing primary decompositions for powers of $I+J$, and to attacking the persistence problem for associated primes of powers of an ideal. This is joint work with Irena Swanson found on arXiv:1806.03545.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120578&date=2018-10-23Topology Seminar (Introductory Talk), Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120794&date=2018-10-24
The notion of geometrically finite discrete groups are originally defined by Ahlfors for subgroups of isometries of the 3-dimensional hyperbolic space, and alternative definitions of geometric finiteness were later given by Marden, Beardon and Maskit, and Thurston. We will focus on the definition given by Beardon and Marskit, and review Bishop’s characterization of geometrically finite discrete isometry subgroups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120794&date=2018-10-24Constructing (2+1)-dimensional KPZ evolutions, Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120826&date=2018-10-24
The (d+1)-dimensional KPZ equation<br />
\[<br />
\partial_t h = \nu \Delta h + \frac{\lambda}{2}|\nabla h|^2 + \sqrt{D}\dot{W},<br />
\]<br />
in which \dot{W} is a space--time white noise, is a natural model for the growth of d-dimensional random surfaces. These surfaces are extremely rough due to the white noise forcing, which leads to difficulties in interpreting the nonlinear term in the equation. In particular, it is necessary to renormalize the mollified equations to achieve a limit as the mollification is turned off. The d = 1 case has been understood very deeply in recent years, and progress has been made in d ≥ 3, but little is known in d = 2. I will describe recent joint work with Sourav Chatterjee showing the tightness of a family of Cole--Hopf solutions to (2+1)-dimensional mollified and renormalized KPZ equations. This implies the existence of subsequential limits, which we furthermore can show do not coincide with solutions to the linearized equation, despite the fact that our renormalization scheme involves a logarithmic attenuation of the nonlinearity as the mollification scale is taken to zero.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120826&date=2018-10-24Topology Seminar (Main Talk), Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120795&date=2018-10-24
In this talk, we focus on negatively pinched Hadamard manifolds which are complete, simply connected Riemannian manifolds with sectional curvature ranging between two negative constants. We use the techniques in geometric groups theory to generalize Bishop’s characterization of geometric finiteness to discrete isometry subgroups of negatively pinched Hadamard manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120795&date=2018-10-24Paris/Berkeley/Bonn/Zürich Analysis Seminar, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120821&date=2018-10-25
Free boundary problems are those described by PDE's that exhibit a priori unknown (free) interfaces or boundaries. The Stefan problem is the most classical and motivating example in the study of free boundary problems. It describes the evolution of a medium undergoing a phase transition, such as ice passing to water. A milestone in this context is the classical work of Caffarelli (Acta Math. 1977), in which he established for the first time the regularity of free boundaries in the Stefan problem, outside a certain set of singular points. The goal of this talk is to present some new results concerning the size of the singular set in the Stefan problem, proving in particular that, in $\mathbb R^3$, for almost every time the free boundary is smooth, with no singularities. This is a joint work with A. Figalli and J. Serra.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120821&date=2018-10-25Applied Math Seminar, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120676&date=2018-10-25
A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for ordinary differential equations, sparse identification for partial differential equations with or without parametric dependencies, and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120676&date=2018-10-25Berkeley Writers at Work, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119337&date=2018-10-25
Edward Frenkel, Professor of Mathematics, will be the featured writer in the Fall 2018 Berkeley Writers at Work series. The event will take place on Thursday, October 25, from noon to 1:30 pm in the Morrison Library, 101 Main Library, on the UC Berkeley campus.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119337&date=2018-10-25Mathematics Department Colloquium, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120265&date=2018-10-25
Khovanov and Rozansky introduced a link homology theory which categorifies the HOMFLY polynomial. This invariant has a lot of interesting properties, but it is notoriously hard to compute. I will discuss recent progress in understanding HOMFLY homology and its surprising relation to algebraic geometry of the Hilbert scheme of points on the plane. The talk is based on joint works with Matt Hogancamp, Andrei Negut and Jacob Rasmussen.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120265&date=2018-10-25Probabilistic Operator Algebra Seminar, Oct 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120822&date=2018-10-30
I will present my recent results on operators on $L^p$ and $l^p$. These include (1) a characterization of the weak closure of ultrapowers of operators on $L^p$ and (2) $l^p$ versions of some results in the Brown-Douglas-Fillmore theory. Some applications will be shown: (1) ultrapowers of operators on $L^p$ have exactly 4 nontrivial invariant subspaces if the ultrafilter is selective (2) every unital homomorphism from C(M) into the Calkin algebra of $l^p$ can be expressed as a compression of a unital homomorphism from $C(M)$ into $B(l^p)$. Proofs of certain results are sketched. Some of the proofs are based on the proofs for Hilbert space and a probabilistic construction. However, the proof of homotopy invariance of the $Ext^-1$ group for $l^p$ uses an approach different from Kasparov's KK-theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120822&date=2018-10-30Rigidity and tolerance for perturbed lattices, Oct 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120793&date=2018-10-31
Consider a perturbed lattice {v+Y_v} obtained by adding IID d-dimensional Gaussian variables {Y_v} to the lattice points in Z^d. <br />
Suppose that one point, say Y_0, is removed from this perturbed lattice; is it possible for an observer, who sees just the remaining points, to detect that a point is missing?<br />
In one and two dimensions, the answer is positive: the two point processes (before and after Y_0 is removed) can be distinguished using smooth statistics, analogously to work of Sodin and Tsirelson (2004) on zeros of Gaussian analytic functions. (cf. Holroyd and Soo (2011) ). The situation in higher dimensions is more delicate; our solution depends on a game-theoretic idea, in one direction, and on the unpredictable paths constructed by Benjamini, Pemantle and the speaker (1998), in the other. (Joint work with Allan Sly).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120793&date=2018-10-31Tales from the front lines of wrangling earth science data, Nov 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120054&date=2018-11-06
Building the data capabilities and products needed to help enable understanding of watershed dynamics, tropical forests, carbon flux, and soil carbon. are just a few of the areas where we are working. This talk will describe the role inter-disciplinary data science is playing in helping to address these challenges. Many challenges encountered are not addressed by the tools available today.<br />
<br />
The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120054&date=2018-11-06Seminar 217, Risk Management: Topic Forthcoming, Nov 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118744&date=2018-11-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118744&date=2018-11-13Integrating eco-evolutionary data from islands to infer biodiversity dynamics, Nov 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120056&date=2018-11-13
A central challenge in understanding the origins of biodiversity is that, while we can observe and test local ecological phenomena, we must usually infer the longer-term outcomes of these ecological forces indirectly. My colleagues and I have been developing inferential models at the interface between macroecology and population-level processes, and applying them to data from geological chronosequences that present communities of different ages. Inferences from these “snapshots in time” provide a link between direct observational methods for local communities and models that make indirect inferences underlying community history. We use data from multiple insular systems, each comprising replicated sites that range from 5 million years. In this way we can directly link ecological theories and models of community composition within a temporal framework so as to understand the history underlying patterns of species diversity. The approach bridges ecological and evolutionary theory to provide a framework for making predictions about biodiversity dynamics.<br />
<br />
The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120056&date=2018-11-13Arithmetic Geometry and Number Theory RTG Seminar, Nov 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120474&date=2018-11-19
Methods of $p$-adic analysis provide the most powerful tools to bound the set of rational points on a curve. The earliest work in this direction was the method of Chabauty; in many cases this is already enough to enumerate (with proof) the rational points. Much more recently, work of Kim on the unipotent fundamental group has led to computational breakthroughs by Balakrishnan, Dogra et al. The method of Chabauty works only when $r < g$ (here $r$ is the rank of the Jacobian, and $g$ the genus of the curve); Kim's method has been applied to the case $r = g$, though it is expected to apply in general. I will discuss a new method for bounding points on curves, using instead a reductive representation of the fundamental group. This new method may apply to all curves, but it presents substantial computational difficulties.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120474&date=2018-11-19The Limits of Proof, Nov 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120718&date=2018-11-19
In the early part of the 20th century, Gödel, Turing, and Tarski showed that no consistent system of reasoning can contain proofs of important properties of the natural numbers or of computations. In these cases, the difficulty stems from the need to reason about infinities of numbers or time that don't show up in our everyday world. In contrast, proofs of properties in a bounded size world always exist.<br />
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The field of proof complexity studies the power of the many ways to express such proofs. These ways involve logic, algebra, combinatorial optimization, graph theory, and computations.<br />
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For many natural properties and methods of reasoning from these diverse fields, one can show that, though proofs exist, their sizes must be astronomical – even proofs about small worlds would require more symbols to write down than there are particles in the universe.<br />
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I will survey highlights and research directions in proof complexity and how these have implications for the P versus NP question and beyond.<br />
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Light refreshments will be served before the lecture at 3:30 p.m.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120718&date=2018-11-19Seminar 217, Risk Management: Topic Forthcoming, Nov 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118746&date=2018-11-27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118746&date=2018-11-27Creating the future of nuclear energy, Nov 27
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120057&date=2018-11-27
The nuclear energy industry is at a crossroads: existing nuclear reactors are struggling to operate economically in some tough markets, and construction of new designs in the U.S. is slow and over budget. At the same time, interest in and development of the next generation of nuclear reactors is growing at an unprecedented rate, and some other nations are building new reactors efficiently. Can the current fleet reduce costs? Will the next generation of designs be “walkaway safe” and cost-competitive? What about safeguards and recycling of nuclear fuel? Many new technologies, including Data Analytics and Machine Learning, can be impactful in answering these questions. This talk will frame some of the big challenges in nuclear energy and how new technologies are starting to be used. We’ll also look to the future in terms of where the biggest impacts are likely to be and what we can do to move quickly.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120057&date=2018-11-27Maps of a rising water table: The hidden component of sea level rise, Dec 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120058&date=2018-12-04
Map-based data viewers have been available for several years that reveal where coastal flooding is likely to occur as oceans warm and ice sheets melt. Recently, geologists have begun to study the influence of sea level rise on groundwater, and have concluded that in some coastal areas, as much or more land could flood as a result of rising groundwater than will flood directly from saltwater. Yet almost no coastal areas have maps available of depth to the water table, below which soils are saturated with water. My students and I have recently made a map of depth to the water table around San Francisco Bay, and this map reveals previously unrecognized vulnerabilities to sea level rise. By taking groundwater into account, we have revealed some potential problems with adaptation that relies on seawalls and levees alone, and developed an alternative strategy for urban areas that might allow us to live with higher water. This talk will present both the new maps of coastal groundwater depth and some strategies for urban adaptation.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120058&date=2018-12-04