Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124805&date=2019-04-01
Cluster algebras were introduced and studied in a series of articles by Fomin and Zelevinsky in [FZ02,FZ03,FZ07] and by Berenstein–Fomin–Zelevinsky in [BFZ05]. They admit connections to several branches of mathematics such as representation theory, geometry, and combinatorics. These algebras are defined by generators obtained recursively form an initial data (a quiver or a matrix). During this talk we will define cluster algebras and show examples. Provided the cluster algebra is acyclic (hence it is a Krull domain), we will show how to compute the associated class group just by looking at the initial data. As a result, we determine when a cluster algebra is a unique factorization domain. Eventually, such proofs rest entirely on tableau combinatorics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124805&date=2019-04-01Berkeley Statistics and Machine Learning Forum, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124350&date=2019-04-01
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
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The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124350&date=2019-04-01String-Math Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124650&date=2019-04-01
Based on the representation theory of quantum toroidal algebras we propose a generalization of the refined topological vertex formalism incorporating additional "Higgsed" vertices and lines apparently corresponding to refined Lagrangian branes. We find rich algebraic structure associated to brane diagrams incorporating the new vertices and lines. In particular, we build the screening charges associated to W-algebras of types \(gl(n)\) and \(gl(n|m)\), and more generally to Y-algebras of Gaiotto and Rapcak. The resulting refined partition functions coincide with partition functions of certain interacting 5d-3d-1d systems of quiver gauge theories (including quivers associated with superalgebras). Our formalism also automatically incorporates Ruijsenaars-Schneider Hamiltonians and their supersymmetric generalizations which act on the refined partition functions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124650&date=2019-04-01Northern California Symplectic Geometry Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125010&date=2019-04-01
After sketching the basics of derived algebraic geometry, I will explain how to define symplectic and lagrangian structures in this setting. A derived symplectic structure has a “shift” (or degree) that is zero for usual symplectic structures. This degree allows us a greater freedom, e.g. it leads to the fact that the derived intersection of two usual lagrangians is symplectic with a $-1$ shift. I will describe the basic existence theorems for symplectic structures on derived moduli spaces.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125010&date=2019-04-01Arithmetic Geometry and Number Theory RTG Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124367&date=2019-04-01
I will show a new, simple construction of crystals associated with toric hypersurfaces and exploit it to prove p-adic congruences for expansion coefficients of rational functions. This is joint work with Frits Beukers.<br />
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The exposition will be self-contained, but I shall explain that our ideas evolve from those of Bernard Dwork. Since he constructed an explicit Frobenius operator which does point counting for hypersurfaces, attempts to give a cohomological interpretaion of Dwork's work resulted in the Monsky–Washnitzer theory. Leaving out the $p$-adic counterpart, in 1990s Batyrev used solely the de Rham aspect of Dwork's theory to study mixed Hodge structure on the middle cohomology of toric hypersurfaces. Our construction basically adds the Frobenius structure back to this picture. As one of the applications, we will do a version of Katz's internal reconstruction of unit-root crystals via expansion coefficients of differential forms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124367&date=2019-04-01Differential Geometry Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124649&date=2019-04-01
We will give a brief review of the study of collapsed Riemannian manifolds with sectional curvature bounds, and we will report some recent progress on collapsed manifolds with Ricci curvature and local rewinding volume bounded below.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124649&date=2019-04-01Northern California Symplectic Geometry Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125011&date=2019-04-01
In previous work, Hutchings, Ramos and I studied the embedded contact homology (ECH) spectrum for any closed three-manifold with a contact form, and proved a “volume identity” showing that the leading order asymptotics recover the contact volume. I will explain recent joint work that sharpens this asymptotic formula by estimating the subleading term. The main technical point needed in our work is an improvement of a key spectral flow bound in Taubes' proof of the three-dimensional Weinstein conjecture; the main goal of my talk will be to explain the ideas that go into this improvement. I will also discuss some possibilities for obtaining sharp asymptotics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125011&date=2019-04-01Analysis and PDE Seminar, Apr 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124368&date=2019-04-01
Carleson proposed a problem on a.e. convergence for free Schrödinger solutions as time goes to zero. Recently it got a sharp answer (up to the endpoint) in all dimensions. We will talk about the new result in dimensions $n+1$ for all $n >2$ and ideas behind it (joint work with Xiumin Du).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124368&date=2019-04-01Seminar 217, Risk Management: Robust Experimentation in the Continuous Time Bandit Problem, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122093&date=2019-04-02
We consider the experimentation dynamics of a decision maker (DM) in a two-armed bandit setup, where the agent holds ambiguous beliefs regarding the distribution of the return process of one arm and is certain about the other one. The DM entertains Multiplier preferences a la Hansen and Sargent [2001], thus we frame the decision making environment as a two-player differential game against nature in continuous time. We characterize the DM's value function and her optimal experimentation strategy that turns out to follow a cut-off rule with respect to her belief process. The belief threshold for exploring the ambiguous arm is found in closed form and is shown to be increasing with respect to the ambiguity aversion index. We then study the effect of provision of an unambiguous information source about the ambiguous arm. Interestingly, we show that the exploration threshold rises unambiguously as a result of this new information source, thereby leading to more conservatism. This analysis also sheds light on the efficient time to reach for an expert opinion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122093&date=2019-04-02Student Harmonic Analysis and PDE Seminar (HADES), Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124369&date=2019-04-02
The Fourier extension operator is a very interesting and difficult object to study in harmonic analysis. Stein conjectured that it is a bounded linear operator between some $L^p$ spaces. Recently people have found that auxiliary real polynomials can help one study Stein's above Restriction Conjecture. We will talk about a few interesting facts about zero sets of real polynomials, and why they can be useful in the study of the Restriction Conjecture.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124369&date=2019-04-023-Manifold Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125016&date=2019-04-02
We'll describe subgroup separability for arithmetic hyperbolic manifolds of simplest type and apply it to describe embedding results due to Kolpakov-Reid-Slavich. With this we can address a conjecture of Claude LeBrun that the Seiberg-Witten invariants of hyperbolic 4-manifolds vanish, by showing the existence of examples for which it is true. Joint with Francesco Lin.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125016&date=2019-04-02Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124984&date=2019-04-02
An artinian local ring $(R,m)$ is called Gorenstein if it has a unique minimal ideal. If $R$ is graded, then it is called Koszul if $R/m$ has a linear $R$-free resolution. Any Koszul algebra is defined by quadratic relations, but the converse is false, and no one knows a finitely computable criterion. Both types of rings occur in many situations in algebraic geometry and commutative algebra, and in many cases, a Gorenstein quadratic algebra coming from geometry is often Koszul (e.g. homogeneous coordinate rings of most canonical curves).<br />
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In 2001, Conca, Rossi, and Valla asked the question: must a (graded) quadratic Gorenstein algebra of regularity 3 be Koszul?<br />
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I will talk about techniques for deciding whether a quadratic Gorenstein algebra is Koszul and methods for generating many examples which are not Koszul. We will explain how these methods provide a negative answer to the above question, as well as a complete picture in the case of regularity at least 4. (This is joint work with Hal Schenck and Matt Mastroeni).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124984&date=2019-04-02Tajima coalescent, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124950&date=2019-04-02
In this talk I will present the Tajima coalescent, a model on the ancestral relationships of molecular samples. This model is then used as a prior model on unlabeled genealogies to infer evolutionary parameters with a Bayesian nonparametric method. I will then show that conditionally on observed data and a particular mutation model, the cardinality of the hidden state space of Tajima’s genealogies is exponentially smaller than the cardinality of the hidden state space of Kingman’s genealogies. We estimate the corresponding cardinalities with sequential importance sampling. Finally, I will propose a new distance on unlabeled genealogies that allows us to compare different distributions on unlabeled genealogies to Tajima’s coalescent.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124950&date=2019-04-02Representation Theory and Mathematical Physics Seminar, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125008&date=2019-04-02
We present a solution of the matrix Bochner problem, a long-standing open problem in the theory of orthogonal polynomials, with applications to diverse areas of research including representation theory, random matrices, spectral theory, and integrable systems. Our solution is based on ideas applied by Krichever, Mumford, Wilson and others, wherein the algebraic structure of an algebra of differential operators influences the values of the operators within the algebra. By using a similar idea, we convert the matrix Bochner problem to one about noncommutative algebras of GK dimension 1 which are module finite over their centers. Then the problem is resolved using the representation theory of these algebras.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125008&date=2019-04-02CANCELED: Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124985&date=2019-04-02
I will tell the story of equivariant completion of toric varieties and their degenerations from the perspectives of algebraic geometry and combinatorics. We will start on the algebraic geometry side with results of Nagata and Sumihiro on completions of varieties. We will then move on to later combinatorial proofs that normal toric varieties admit completions. Finally, we will discuss recent results which show that certain degenerations of toric varieties admit equivariant completions. We will see that, in contrast to the earlier part of the story, the algebraic-geometric proof does not show the existence of normal equivariant completions, whereas the combinatorial proof does.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124985&date=2019-04-02Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124992&date=2019-04-02
After reviewing classical results about existence of completions of varieties, I will talk about a class of degenerations of toric varieties which have a combinatorial classification - normal toric varieties over rank one valuation rings. I will then discuss recent results about the existence of equivariant completions of such degenerations. In particular, I will show a new result about the existence of normal equivariant completions of these degenerations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124992&date=2019-04-02Topology Seminar (Introductory Talk), Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124990&date=2019-04-03
Part of the Deligne–Mumford compactification of the moduli space of marked Riemann surfaces comes from the collision of marked points ("bubbling"). I will explain this kind of degeneration and then talk about a real analogue of such compactification in the study of constant curvature conical metrics, where a similar bubbling behavior appears.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124990&date=2019-04-03Deformation Theory Seminar, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125064&date=2019-04-03
We will review Orlov’s construction of an equivalence of categories between certain Calabi-You complete intersection in weighted protective spaces and the equivariant matrix factorization of associated quasihomogeneois singularitieshttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125064&date=2019-04-03Grace-like polynomials and related questions, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124979&date=2019-04-03
We say that the multi-affine polynomial P(z1, . . . , zm, w1, . . . , wn) is Grace-like if it does not vanish when {z1, . . . , zm is separated from {w1, . . . , wn) by a circle in the complex plane. Such polynomials have many unexpected probabilistic properties related to the work of Borcea-Brändén.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124979&date=2019-04-03Number Theory Seminar, Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125015&date=2019-04-03
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125015&date=2019-04-03Topology Seminar (Main Talk), Apr 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124991&date=2019-04-03
The problem of finding and classifying constant curvature metrics with conical singularities has a long history bringing together several different areas of mathematics. This talk will focus on the particularly difficult spherical case where many new phenomena appear. When some of the cone angles are bigger than $2\pi $, uniqueness fails and existence is not guaranteed; smooth deformation is not always possible and the moduli space is expected to have singular strata. I will give a survey of several recent results regarding this singular uniformization problem, connecting PDE techniques with complex analysis and synthetic geometry. Based on joint works with Rafe Mazzeo and Bin Xu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124991&date=2019-04-03Applied Math Seminar, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124539&date=2019-04-04
Adversarial path planning problems are important in robotics applications and in modeling the behavior of humans in dangerous environments. Surveillance-Evasion (SE) games form an important subset of such problems and require a blend of numerical techniques from multiobjective dynamic programming, game theory, numerics for Hamilton-Jacobi PDEs, and convex optimization. We model the basic SE problem as a semi-infinite zero-sum game between two players: an Observer (O) and an Evader (E) traveling through a domain with occluding obstacles. O chooses a pdf over a finite set of predefined surveillance plans, while E chooses a pdf over an infinite set of trajectories that bring it to a target location. The focus of this game is on "E's expected cumulative exposure to O", and we have recently developed an algorithm for finding the Nash Equilibrium open-loop policies for both players. I will use numerical experiments to illustrate algorithmic extensions to handle multiple Evaders, moving Observes, and anisotropic observation sensors. Time permitting, I will also show preliminary results for a very large number of selfish/independent Evaders modeled via Mean Field Games.<br />
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Joint work with M.Gilles, E.Cartee, and REU-2018 participants.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124539&date=2019-04-04Statistical and Computational Challenges in Conformational Biology, Apr 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125018&date=2019-04-04
Chromatin architecture is critical to numerous cellular processes including gene regulation, while conformational disruption can be oncogenic. Accordingly, discerning chromatin configuration is of basic importance, however, this task is complicated by a number of factors including scale, compaction, dynamics, and inter-cellular variation.<br />
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The recent emergence of a suite of proximity ligation-based assays, notably Hi-C, has transformed conformational biology with, for example, the elicitation of topological and contact domains providing a high resolution view of genome organization. Such conformation capture assays provide proxies for pairwise distances between genomic loci which can be used to infer 3D coordinates, although much downstream analysis bypasses this reconstruction step.<br />
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After demonstrating advantages deriving from obtaining 3D genome reconstructions, in particular from superposing genomic attributes on a reconstruction and identifying extrema (â€™3D hotspotsâ€™) thereof, we showcase methodological challenges surrounding such analyses, as well as advancing a novel reconstruction approach based on principal curves. Open issues highlighted include (i) performing and synthesizing reconstructions from single-cell assays, (ii) devising rotation invariant methods for 3D hotspot detection, (iii) assessing genome reconstruction accuracy, and (iv) averting reconstruction uncertainty by direct integration of Hi-C data and genomic features. By using p-values from (epi)genome wide association studies as the feature the latter approach provides a conformational lens for viewing GWAS findings.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125018&date=2019-04-04'Information and Uncertainty in Data Science' Discussion Forum, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124354&date=2019-04-05
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
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The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124354&date=2019-04-05Student Probability/PDE Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125014&date=2019-04-05
For $\alpha >0$, the $\alpha$-Lipschitz minorant of a càdlàg function f is the greatest $\alpha$-Lipschitz function that is dominated by f. We study the joint law of any two-sided Lévy process $(X_t)_{t \in \mathbb R}$ and its $\alpha$-Lipschitz minorant $(M_t)_{t \in \mathbb R}$. In particular, we consider $\mathcal Z$ to be the set of points where $X$ meets $M$, and prove that $((X_t),\mathcal Z)$ is a stationary and regenerative space-time system. Under some determined conditions, when the set $\mathcal Z$ is almost surely discrete, we have an i.i.d sequence of excursions of X above M. In the special case, when X is a Brownian motion with drift, we give explicit path decompositions of those excursions. This $\alpha$-Lipschitz minorant appears as the solutions of the Hamilton-Jacobi PDE when the initial condition is a Lévy noise and the corresponding Lagrangian is of the form $L(v)=\alpha \vert v \vert$. This talk is based on a joint work with Steven N. Evans.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125014&date=2019-04-05Special Quantum Geometry Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125069&date=2019-04-05
Assuming that both temperature and pressure are continuous functions, we can conclude that there are always two antipodal points on Earth with exactly the same pressure and temperature. This is the two-dimensional version of the celebrated Borsuk-Ulam Theorem which states that for any continuous map from the n-dimensional sphere to n-dimensional real Euclidean space there is always a pair of antipodal points on the sphere that are identified by the map. Our quest to unravel topological mysteries in the Middle Earth of quantum spaces will begin with gentle preparations in the Shire of elementary topology. Then, after riding swiftly through the Rohan of C*-algebras and Gelfand-Naimark Theorems, and carefully avoiding the Mordor of incomprehensible technicalities, we shall arrive in the Gondor of compact quantum groups acting freely on unital C*-algebras. It is therein that the noncommutative Borsuk-Ulam-type conjecture dwells waiting to be proven or disproven. After revealing how to prove the conjecture assuming some torsion or local-triviality properties, we shall explain how the general case (no torsion or local-triviality assumptions) implies the famous and long-standing weak Hilbert-Smith conjecture. To end with, we will explain how a certain special case of the conjecture can be interpreted as the non-contractibility of non-trivial compact quantum groups, and prove it for some classes of compact quantum groups. (Based on joint works with Paul F. Baum, Ludwik Dabrowski, Eusebio Gardella, Sergey Neshveyev, Mariusz Tobolski and Jianchao Wu.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125069&date=2019-04-05Deformation Theory Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125065&date=2019-04-05
We will discuss the appearance of superpotentials for matrix factorizations from the symplectic side of Mirror Symmetry in the SYZ construction, with the monomial terms corresponding to components of the canonical boundary divisor.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125065&date=2019-04-05Logic Colloquium, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124610&date=2019-04-05
I will present some recent applications of Model Theory to uniform bounds in questions arising from Number Theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124610&date=2019-04-05Student 3-Manifold Seminar, Apr 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125122&date=2019-04-05
Compact surfaces with non-positive Euler characteristic can be inductively decomposed by cutting along finitely many properly embedded loops and arcs until one is left with a collection of disks; such a decomposition is called a hierarchy. An analogue up a dimension is called a Haken manifold, which can be inductively decomposed by cutting along two-sided incompressible surfaces until one is left with a collection of balls. Examples of Haken manifolds include link complements and surface bundles over circles. Certain facts about Haken manifolds can be proved by induction on a hierarchy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125122&date=2019-04-05Probabilistic Operator Algebra Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124538&date=2019-04-08
Chordal Loewner equations have been shown to be connected with evolution equations for semigroups in monotone probability. I will briefly recall these connections and then discuss recent related work of Franz, Hasebe and Schleissinger which uses these connections to probability measures on $\mathbb R$ with univalent Cauchy transform and some of the analytic and geometric properties thereof. Time permitting, I will also discuss results in the multiplicative setting.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124538&date=2019-04-08Combinatorics Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124983&date=2019-04-08
We provide an insertion algorithm from generalized permutations (or two-line arrays subject to certain conditions) and pairs of standard Young tableaux and multiset tableaux of the same shape. If we insert the propagating blocks of partition diagrams we get natural sets of tableaux and the number of these tableaux of a fixed shape are equal to the dimensions of irreducible representations indexed by the same shape. This is joint work with Laura Colmenarejo, Rosa Orellana, Franco Saliola and Mike Zabrocki.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124983&date=2019-04-08Arithmetic Geometry and Number Theory RTG Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125099&date=2019-04-08
The Birch and Swinnerton-Dyer conjecture is known in the case of rank 0 and 1 thanks to the foundational work of Kolyvagin and Gross-Zagier. In this talk, I will report on a joint work in progress with Yifeng Liu, Yichao Tian, Wei Zhang, and Xinwen Zhu. We study the analogue and generalizations of Kolyvagin's result to the unitary Gan-Gross-Prasad paradigm. More precisely, our ultimate goal is to show that, under some technical conditions, if the central value of the Rankin-Selberg L-function of an automorphic representation of U(n)*U(n+1) is nonzero, then the associated Selmer group is trivial; Analogously, if the Selmer class of certain cycle for the U(n)*U(n+1)-Shimura variety is nontrivial, then the dimension of the corresponding Selmer group is one.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125099&date=2019-04-08Differential Geometry Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125009&date=2019-04-08
Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the interior of the Kähler cone must have a convergent subsequence. As an application, we prove the existence of global moduli spaces of scalar-flat Kähler ALE metrics for several infinite families of Kähler ALE spaces. Joint with J. Viaclovskyhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125009&date=2019-04-08David Morton — Models and Algorithms for Multi-stage Stochastic Programming, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125022&date=2019-04-08
Abstract: We consider two classes of multi-stage stochastic linear programs (MSLPs) that lend themselves to solution by stochastic dual dynamic programming (SDDP). First, we consider a distributionally robust MSLP. Here, the specific realizations in each stage are fixed, and distributional robustness is with respect to the probability mass function governing those realizations. Second, we consider a class of partially observable MSLPs. In both cases, we describe a computationally tractable variant of SDDP to solve the model. This is joint work with Oscar Dowson, Daniel Duque, and Bernardo Pagnoncelli.Bio: David Morton is the David A. and Karen Richards Sachs Professor and Department Chair of Industrial Engineering & Management Sciences at Northwestern University. He received his PhD in Operations Research from Stanford University. He was a Fulbright Research Scholar at Charles University in Prague, a National Research Council Postdoctoral Fellow in the Operations Research Department at the Naval Postgraduate School, and is an INFORMS Fellow.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125022&date=2019-04-08Analysis and PDE Seminar, Apr 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123670&date=2019-04-08
I will explain how the results of Bourgain, Burq and the speaker '13 can be used to obtain control and observability by rough functions and sets on 2-tori. We show that for the time dependent Schrödinger equation, any set of positive measure can be used for observability and controllability. For non-empty open sets this follows from the results of Haraux '89 and Jaffard '90, while for sufficiently long times and rational tori this can be deduced from the results of Jakobson '97. Other than tori (of any dimension; cf. Komornik '91, Anantharaman–Macia '14) the only compact manifolds for which observability holds for any non-empty open sets are hyperbolic surfaces. That follows from results of Bourgain–Dyatlov '16 and Dyatlov–Jin '17 and I will discuss the difficulty of passing to rougher rougher sets in that case. Joint work with N Burq.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123670&date=2019-04-08CANCELED: Seminar 217, Risk Management: No Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122094&date=2019-04-09
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122094&date=2019-04-09Student Harmonic Analysis and PDE Seminar (HADES), Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125007&date=2019-04-09
I will present a microlocal approach to some of the analytical problems in hyperbolic dynamics. Applications include exponential decay of correlations and a definition of Pollicott-Ruelle resonances for hyperbolic systems. The intuition comes from scattering theory, with scattering happening as frequency goes to infinity. Based on joint work with Maciej Zworski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125007&date=2019-04-093-Manifold Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125141&date=2019-04-09
We’ll introduce some preliminaries such as Hodge theory and spin structure for Seiberg-Witten invariants on 4-manifolds. Then a nice nonlinear PDE on the spin bundle of 4-manifolds will give rise to a moduli space related to Seiberg-Witten invariants. We will also discuss some related results of hyperbolic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125141&date=2019-04-09Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125117&date=2019-04-09
One consequence of the recent push to develop a scheme theory in tropical geometry has been the development of a tropical commutative algebra. This starts with the commutative algebra of semirings, but in order to get a theory that interacts with geometry, we are lead to impose some combinatorial, matroid-theoretic, conditions. I will introduce these ideas, and discuss the current state of our understanding.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125117&date=2019-04-09Representation Theory and Mathematical Physics Seminar, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125135&date=2019-04-09
Spherical varieties are algebraic varieties with an action by a reductive group which admit an open Borel orbit. This extra condition on its symmetries connects their study to representation theory, makes tractable their classification, and yet is broad enough to have many rich examples.<br />
<br />
We introduce a definition of a spherical supervariety, which is a simple generalization of the classical definition to the super world. Then, with a focus on the affine case, we look at certain properties of these spaces, highlighting some of the differences and similarities with the classical story.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125135&date=2019-04-09Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125136&date=2019-04-09
Last week Mike Stillman spoke about recent investigations of Koszul algebras. I'll give some more general background on resolutions of the residue field of a local ring, and talk about work of Conca and others on bounds for the syzygies of a Koszul ring.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125136&date=2019-04-09Harmonic Analysis Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125182&date=2019-04-10
The title refers to inequalities of the form $\int _{[0,1]^d} \prod _{j=1}^d f_j(x_j) \,e^{i\lambda \psi (x)}\,dx = O(|\lambda |^{-\gamma } \prod _j \|f_j\|_{L^{p_j}})$ for large $\lambda \in {\mathbb R}$. Here $\psi :{\mathbb R}^d\to {\mathbb R}$ is a smooth phase function, and the exponent γ depends on ψ and on the exponents $p_j$. These inequalities are well understood in the bilinear case $d=2$, and sharp bounds have been obtained by Phong-Stein-Sturm and Gilula-Gressman-Xiao for certain parameter ranges for $d >2$. Nonetheless, the case $d\ge 3$ remains largely mysterious. I will argue that the most basic question in this context remains unaddressed for $d\ge 3$, and will present recent partial results and examples for $d=3$ with an outline of the proofs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125182&date=2019-04-10Topology Seminar (Introductory Talk), Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125012&date=2019-04-10
Given a pseudo-Anosov mapping class of a closed orientable surface, there exists a finite cover of the surface to which the mapping class lifts, such that the induced action on the first homology has at least one eigenvalue lying outside of the unit circle. In this talk, I will review some background related to the above result, and its relations with twisted Reidemeister torsion and Fried's cone of homological directions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125012&date=2019-04-10Deformation Theory Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125181&date=2019-04-10
We will review the theory of curved deformations, based largely on a recent paper by Blanc-Katzarkov-Pandit and earlier work of Preygel. (Mind that the Hill shuttle is not running this Wednesday!)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125181&date=2019-04-10Bigeodesics in first and last passage percolation, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125095&date=2019-04-10
First and last passage percolation are statistical physics models of<br />
random growth. These models are widely believed to belong to the<br />
Kardar-Parisi-Zhang universality class. I will define these two models<br />
and talk about what it means to be in this universality class. A<br />
longstanding question about these models is whether they have<br />
bi-infinite geodesics. This question is of interest to physicists due<br />
to its connections to the Ising model. I will discuss the recent<br />
progress on this question. This talk is based on joint work with<br />
Daniel Ahlberg, Riddhipratim Basu and Allan Sly.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125095&date=2019-04-10BIDS Data Science Lecture: Do as eye do: efficient content-adaptive processing and storage of large fluorescence images, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124344&date=2019-04-10
Modern microscopes create a data deluge with gigabytes of data generated each second, and terabytes per day. Storing and processing this data is a severe bottleneck, not fully alleviated by data compression. We argue that this is because images are processed as grids of pixels. To address this, we developed a content-adaptive representation of fluorescence microscopy images, the Adaptive Particle Representation (APR). The APR replaces pixels with particles positioned according to image content. The APR not only overcomes storage bottlenecks, as data compression does, but additionally overcomes memory and processing bottlenecks since the adaptivity can be used during processing tasks. In this talk, I will introduce the ideas and concepts of the APR, its performance on experimental data, and show how the APR can be used to enhance, rather than replace, existing algorithms and approaches, including applications to machine learning. Beyond image-processing I will also present how the APR can be used for adaptive resolution simulations, and discuss work on robust methods for data-driven model discovery for spatial-temporal data.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124344&date=2019-04-10Number Theory Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125100&date=2019-04-10
The Farey fractions of level $n$ are the set of rationals in $[0,1]$ in lowest terms having denominator at most $n$. It is known that a measure of equally weighted point masses (of total mass 1) on the points of the Farey sequence $F_n$ converges to the uniform distribution on $[0,1]$ as $n$ goes to infinity. The Riemann hypothesis is equivalent to suitably fast rates of convergence (to zero) of certain statistics measuring distance to uniform distribution, given by theorems of Franel (1924) and Landau (1924) . This talk addresses a toy model consisting of unreduced Farey fractions (allowing fractions not in lowest terms) and studies similar statistics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125100&date=2019-04-10Renewable Estimation and Incremental Inference in Generalized Linear Models with Streaming Data, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124960&date=2019-04-10
I will present a new statistical paradigm for the analysis of streaming data based on renewable estimation and incremental inference in the context of generalized linear models. Our proposed renewable estimation enables us to sequentially update the maximum likelihood estimation and inference with current data and summary statistics of historic data, but with no use of any historic raw data themselves. In the implementation, we design a new data flow, called the Rho architecture to accommodate the data storage of current and historic data, as well as to communicate with the computing layer of the Spark system in order to facilitate sequential learning. We establish both estimation consistency and asymptotic normality for the renewable estimation and incremental inference for regression parameters. We illustrate our methods by numerical examples from both simulation experiments and real-world analysis. This is a joint work with Lan Luo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124960&date=2019-04-10Representation Theory and Mathematical Physics Seminar, Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124993&date=2019-04-10
The problem of constructing global action-angle variables on coadjoint orbits of compact Lie groups is one of the interesting questions in the theory of integrable systems. A fundamental contribution was made by Guillemin-Sternberg who constructed the Gelfand-Zeitlin integrable systems on coadjoint orbits of the groups \(SU(n)\) and \(SO(n)\). Recently, toric degeneration techniques allowed for the construction of global action-angle variables on rational coadjoint orbits of compact Lie groups of all types.<br />
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In this talk, I will present a new approach which aims at constructing global action-angle coordinates on all regular coadjoint orbits of compact Lie groups and on a large family of related Hamiltonian spaces. It combines the results of Ginzburg-Weinstein on the theory of Poisson-Lie groups and the theory of cluster algebras using the "partial tropicalization” procedure.<br />
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The talk is based on joint works with A. Alekseev, A. Berenstein, B. Hoffman, and J. Lane.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124993&date=2019-04-10Topology Seminar (Main Talk), Apr 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125013&date=2019-04-10
Given a mapping class of a closed orientable surface, we look at any lift of the mapping class to any finite cover of the surface. An eigenvalue of the induced homological action of the lift will be called a virtual homological eigenvalue. How much about the mapping class can we learn through virtual homological eigenvalues? In this talk, I will discuss some results related to this question. In particular, I will present some ways to combine the Nielsen fixed point theory with the more recent virtual specialization techniques in 3-manifold topology.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125013&date=2019-04-10Mathematics Department Colloquium, Apr 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124948&date=2019-04-11
A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions.There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff type surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems. Joint works with A. Ghosh and with J. Bourgain and A. Gamburd.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124948&date=2019-04-11Bay Area Microlocal Analysis Seminar, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124751&date=2019-04-12
Consider the semiclassical Schrödinger equation $(h^2\Delta +V-E)u=0$, where, instead of being smooth, $V$ is allowed to be singular across a hypersurface. The singularity in the potential turns out to have very interesting consequences for the structure of solutions $u$; in effect, WKB solutions include not just contributions from classical propagation across the interface but also reflected singularities, in what amounts to a quantum diffraction effect (meaning one that is not visible at the level of classical Hamiltonian dynamics). I will discuss the propagation and reflection of semiclassical singularities in this setting, and also its consequences for the existence of quantum resonances in systems where trajectories escape to infinity under classical flow but not under the branched flow where we allow reflections. This is joint work with Oran Gannot.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124751&date=2019-04-12Student Probability/PDE Seminar, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125179&date=2019-04-12
We present the work of Armstrong, Cardaliaguet, and Souganidis, who prove convergence rates for stochastic homogenization using a mixture of probability techniques and PDE techniques. We discuss the metric problem, its rate of convergence, its relation to approximate correctors, and the reduction of the full problem to that of approximate correctors.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125179&date=2019-04-12Bay Area Microlocal Analysis Seminar, Apr 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124809&date=2019-04-12
We discuss the recent developments in the inverse length spectral theory of smooth strictly convex domains, including the works of Avila–De Simoi–Kaloshin and Kaloshin–Sorrentino on the Birkhoff conjecture, and De Simoi–Kaloshin–Wei on the length spectral rigidity of nearly circular domains with a reflectional symmetry. In a joint work with Zelditch we explore the inverse Laplace spectral problem for nearly circular ellipses, among all smooth domains without any symmetry or convexity assumption.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124809&date=2019-04-12Combinatorics Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125178&date=2019-04-15
The classical Dehn–Sommerville equations, relating the face numbers of simplicial polytopes, have an analogue for cubical polytopes. These relations can be generalized to apply to simplicial and cubical Eulerian complexes. In this talk, we will introduce a few different known proofs of the classical Dehn–Sommerville relations for simplicial complexes, relating this result to concepts such as zeta polynomials of posets, Ehrhart polynomials of simplicial complexes, and chain-partitions of posets. We will then discuss whether each proof idea can be adapted to the cubical case.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125178&date=2019-04-15Berkeley Statistics and Machine Learning Forum, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124351&date=2019-04-15
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
<br />
The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124351&date=2019-04-15Probabilistic Operator Algebra Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123139&date=2019-04-15
A landmark result of Dykema in 1993 classified free products of tracial finite dimensional von Neumann algebras in terms of interpolated free group factors. In 1997, Shlyakhtenko constructed the free Araki-Woods factors, a natural type III analogue of the free group factors. He asked whether arbitrary free products of non-tracial finite-dimensional von Neumann algebras can always be expressed in terms of free Araki-Woods factors. Partial progress on this problem was obtained by Houdayer and Ueda. In this talk we will answer Shlyakhtenko's question in the affirmative. The key tool we use is a non-tracial free graph von Neumann algebra which will be used to realize some of these free products. This is joint work with Brent Nelson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123139&date=2019-04-15Arithmetic Geometry and Number Theory RTG Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125211&date=2019-04-15
Classical Serre-Tate theory concerns the deformation theory of ordinary abelian varieties. It implies that their deformation spaces can be equipped with a group structure and a lifting of the Frobenius morphism, and consequently such varieties admit a canonical lifting to characteristic zero. In the first half of the talk, aimed at graduate students and people with no prior exposure to the topic, I will review the classical results in this direction.<br />
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In the second half, I will show how to obtain similar results for ordinary Calabi-Yau varieties of arbitrary dimension. The main tools will be Frobenius splittings and Witt vectors of length two. This is joint work with Maciej Zdanowicz (EPFL).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125211&date=2019-04-15Differential Geometry Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125046&date=2019-04-15
We discuss the development on geometric and analytic aspects of the Anomaly flow. Such flow naturally arises in the study of a system of equations for supersymmetric vacua of superstrings proposed independently by C. Hull and A. Strominger in 1980s. The system allows non-vanishing torsion and they incorporate terms which are quadratic in the curvature tensor. As such they are also particularly interesting from the point of view of both non-Kaehler geometry and the theory of nonlinear partial differential equations. It turns out that the corresponding flow shares some features with the Ricci flow and preserves the conformally balanced condition of Hermitian metrics. This talk is based on joint works with D. Phong and S. Picard.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125046&date=2019-04-15Analysis and PDE Seminar, Apr 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125198&date=2019-04-15
In this talk we discuss the problem of global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Several physical models related to general relativity have shown the importance of studying such systems but very few results are known at present in low space dimension, where linear solutions slowly decay in time.<br />
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We study here a model quadratic quasilinear two-dimensional system, in which the nonlinearity writes in terms of “null forms”, and prove global existence by propagating a-priori energy estimates and optimal uniform estimates on the solution. In proving such estimates one has to deal with several issues such as the quasilinear nature of the problem, the very low decay in time of quadratic nonlinearities, the fact that initial data are not compactly supported…<br />
<br />
We will show how to obtain energy estimates by using systematically quasilinear normal forms, in their para-differential version. Uniform estimates will instead be recovered by deducing a new coupled system of a transport equation and an ordinary differential equation from the starting PDE system by means of a semiclassical microlocal analysis of the problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125198&date=2019-04-15Seminar 217, Risk Management: Linking 10-K and the GICS - through Experiments of Text Classification and Clustering, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122096&date=2019-04-16
A 10-K is an annual report filed by a publicly traded company about its financial performance and is required by the U.S. Securities and Exchange Commission (SEC). 10-Ks are fairly long and tend to be complicated. But this is one of the most comprehensive and most important documents a public company can publish on a yearly basis. The Global Industry Classification Standard (GICS) is an industry taxonomy developed in 1999 by MSCI and S&P Dow Jones Indices and is designed to classify a company according to its principal business activity. The GICS hierarchy begins with 11 sectors and is followed by 24 industry groups, 68 industries, and 157 sub-industries. We ask two questions: First, can a classifier be trained to recognize a firm's GICS sector based on the textual information in its 10-K? Second, can we extract, from the classifier, embeddings (low dimensional vectors) for 10-Ks that respect their GICS sectors, so firms within the same sector would have embeddings that are close (measured by cosine similarity)? We report on a series of experiments with Convolutional Neural Network (CNN) for text classification, trained on two variants of document representations, one uses pre-trained word vectors, the other is based on the simple bag-of-words model.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122096&date=2019-04-16Probabilistic Operator Algebra Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125197&date=2019-04-16
A homogeneous noncommutative degree $d$ polynomial $p$ has a $t$-term real Waring (resp. complex Waring) decomposition provided that $p(x)$ can be written as the sum of $t$ terms of the $d^{th}$-power of linear functions of $x$, i.e. \[ p(x)=\sum _{s=1}^t [ A^s_1x_1 + A^s_2x_2 + ... A^s_gx_g]^d \] with real (resp. complex) numbers $A_j^s$. The talk will analyze this, some consequences and extensions.<br />
<br />
If time permits there will be a sketch of some other recent results drawn from free analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125197&date=2019-04-16Student Harmonic Analysis and PDE Seminar (HADES), Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125272&date=2019-04-16
In this talk we will discuss bases in Banach lattices, and how they can be used to measure (non)-embeddability of a Banach space into a lattice. We will give several characterizations of basic sequences that "respect the lattice structure", and discuss some of the more unexpected corollaries. Time permitting, I will comment on existence of non-negative bases in Hilbert space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125272&date=2019-04-16Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125267&date=2019-04-16
Let $R$ be a standard graded algebra over a field. We investigate how the singularities of $\operatorname {Spec} R$ or $\operatorname {Proj} R$ affect the $h$-vector of $R$, which is the coefficients of the numerator of its Hilbert series. The most concrete consequence of our work asserts that if $R$ satisfies Serre's condition $(S_r)$ and have reasonable singularities (Du Bois on the punctured spectrum or $F$-pure), then $h_0,\dots , h_r\geq 0$. Furthermore the multiplicity of $R$ is at least $h_0+h_1+\dots +h_{r-1}$. We also prove that equality in many cases forces $R$ to be Cohen-Macaulay. This is joint work with Linquan Ma and Matteo Varbaro.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125267&date=2019-04-16Representation Theory and Mathematical Physics Seminar, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125067&date=2019-04-16
I will talk about the underlying homotopical structures within field equations, which emerge in string theory as conformal invariance conditions for sigma models. I will show how these, often hidden, structures emerge from the homotopy Gerstenhaber algebra associated to vertex and Courant algebroids, thus making all such equations the natural objects within vertex algebra theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125067&date=2019-04-16Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125268&date=2019-04-16
The Hilbert scheme of n points in $P^2$ is smooth of dimension 2n and the tangent space to any (monomial) ideal admits a nice combinatorial description. On the other hand the Hilbert scheme of n points in $P^3$ is singular and there is a conjecture on what the monomial ideal with the largest tangent space dimension should be. By extending the combinatorial methods used in $P^2$, we give a proof of a major portion of the conjecture (in a sense we will describe). Along the way we will strengthen previous bounds on the dimension of the tangent space. This is joint (ongoing) work with Alessio Sammartano.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125268&date=2019-04-16Harmonic Analysis Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125317&date=2019-04-17
In the first part of the talk, I will outline the proof of the multilinear oscillatory integral inequality that was introduced last week. In the second part we will begin a series of lectures on a new topic, decoupling inequalities, following Bourgain-Demeter and Bourgain-Demeter-Guth.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125317&date=2019-04-17Topology Seminar (Introductory Talk), Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125265&date=2019-04-17
As context for the main talk, we will describe results of Franks and Franks-Handel in surface dynamics and state the ergodic theorem. Two- and three-dimensional dynamics are related via the notions of a global surface of section and open book decomposition, which we will introduce. To close we will discuss the ECH spectral numbers, a three-dimensional construction which can be used to study questions in surface dynamics related to those introduced at the beginning of the talk.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125265&date=2019-04-17Deformation Theory Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125254&date=2019-04-17
I will talk about a new moduli-theoretic interpretation of the spaces of framed little disks, as well as their higher-genus generalization of complex curves with parametrized boundary, as geometric objects over the rational field Q. Applications of this formalism give geometric "explainations" for several results previously proven using transcendental or analytic methods, namely formality of $E_n$ operads, Galois action on Drinfeld associators, and certain relations between "modular" periods and zeta functions proven by Hain.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125254&date=2019-04-17Conformal embedding and percolation on the uniform triangulation, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125260&date=2019-04-17
Following Smirnov’s proof of Cardy’s formula and Schramm’s discovery of SLE, a thorough understanding of the scaling limit of critical percolation on the regular triangular lattice has been achieved. Smirnorv’s proof in fact gives a discrete approximation of the conformal embedding which we call the Cardy embedding. In this talk I will present a joint project with Nina Holden where we show that the uniform triangulation under the Cardy embedding converges to the Brownian disk under the conformal embedding. Moreover, we prove a quenched scaling limit result for the critical percolation on uniform triangulations. Time permitting, I will also explain how this result fits into the the larger picture of random planar maps and Liouville quantum gravity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125260&date=2019-04-17Number Theory Seminar, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125281&date=2019-04-17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125281&date=2019-04-17From correlation to causation — measuring ad effectiveness at scale, Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125235&date=2019-04-17
Everyone has had that one ad for that one pair of shoes seem to follow them everywhere they go on the internet. Why does that happen? Especially if you already bought the shoes? To make sense of this, it's worth understanding how marketers have historically measured ad effectiveness -- and why the problem is harder than it seems. Beyond improvements in measuring ad effectiveness, this talk with dive into the uniquely statistical problems we face in ad tech and some of the ways we are approaching them.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125235&date=2019-04-17Topology Seminar (Main Talk), Apr 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125266&date=2019-04-17
An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the diffeomorphism is the mean action of the orbit. If an area-preserving annulus diffeomorphism is a rotation near the boundary of the annulus, and if its Calabi invariant is less than the maximum boundary value of the action function, then we show that the infimum of the mean action over all periodic orbits of the diffeomorphism is less than or equal to its Calabi invariant.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125266&date=2019-04-17Paris/Berkeley/Bonn/Zürich Analysis Seminar, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125271&date=2019-04-18
I will discuss a joint work with Sergiu Klainerman on the stability of Schwarzschild as a solution to the Einstein vacuum equations with initial data subject to a certain symmetry class.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125271&date=2019-04-18BIDS Data Science Lecture: Astrophysical Machine Learning, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124964&date=2019-04-18
From streaming, repeated, noisy, and distorted images of the sky, time-domain astronomers are tasked with extracting novel science as quickly as possible with limited and imperfect information. Employing algorithms developed in other fields, we have has already reached important milestones demonstrating the speed and efficacy of using ML in data and inference workflows. Now we look to innovations in learning architectures and computational approaches that are purpose-built alongside the specific domain questions. I will describe such efforts—developed in the search for Planet 9, new classes of variable sources, and for data-driven emulators—and discuss on-going efforts to imbue physical understanding into the learning process itself.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124964&date=2019-04-18Mathematics Department Colloquium/Serge Lang Undergraduate Lecture, Apr 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125066&date=2019-04-18
Topologists will say that a coffee cup is like a donut. What do they mean? Homotopy and Homology are invariants created to distinguish basic geometric structures. In this talk I will briefly talk about the history of such invariants and describe new ones that are also applicable to discrete structures like graphs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125066&date=2019-04-18'Information and Uncertainty in Data Science' Discussion Forum, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124355&date=2019-04-19
Full details about this meeting will be posted here: http://compdatascience.org/entropy.<br />
<br />
The 'Information and Uncertainty in Data Science' Discussion Forum is a forum for open inquiry and discussion about a wide range of recurring data science fundamentals, including information, uncertainty, entropy, bits, probability, machine learning, generalization, and others. The group facilitates academic discourse on the practical use of the fundamental concepts across a wide variety of research disciplines, and strives for clarity and understanding using real-world scenarios, visual examples, cutting edge questions and unique perspectives. This group focusses on understanding and sharing concepts that are often buried in mathematical language, especially entropy, reduction of uncertainty and connections between physical systems and information systems. All interested members of the UC Berkeley, UCSF, LBL and LLNL communities are welcome and encouraged to attend. More details available at http://compdatascience.org/entropy. Contact: BIDS Senior Fellow Gerald Friedland.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124355&date=2019-04-19Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125375&date=2019-04-19
I will describe a tropical looking algorithm computing Betti numbers (for intersection cohomology) of moduli spaces of semistable sheaves on the projective plane. This algorithm is an explicit realization of the naive idea of moving in a space of stability conditions and applying a wall-crossing formula. I will also discuss some application to some a priori unrelated question in relative Gromov-Witten theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125375&date=2019-04-19Student Probability/PDE Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125180&date=2019-04-19
We present the work of Armstrong, Cardaliaguet, and Souganidis, who prove convergence rates for stochastic homogenization using a mixture of probability techniques and PDE techniques. We discuss the metric problem, its rate of convergence, its relation to approximate correctors, and the reduction of the full problem to that of approximate correctors.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125180&date=2019-04-19Student Arithmetic Geometry Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125387&date=2019-04-19
I will discuss a paper of Maulik and Poonen on the ranks of Neron-Severi groups of geometric fibers of a smooth proper morphism of varieties over an algebraically closed field of characteristic $0$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125387&date=2019-04-19Student 3-Manifold Seminar, Apr 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125389&date=2019-04-19
We will talk about some of the basic theory of knots and links in $S^3$ with a special focus on the geometry of the complementary space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125389&date=2019-04-19Combinatorics Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125196&date=2019-04-22
The Ehrhart polynomial counts the number of lattice points in integer dilates of a lattice polytope. The h*-polynomial encodes the Ehrhart polynomial in a particular basis. In this talk we give an introduction to the method of interlacing polynomials which is a powerful tool to prove that a polynomial has only real roots and present applications to h*-polynomials of zonotopes and dilated lattice polytopes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125196&date=2019-04-22Probabilistic Operator Algebra Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122407&date=2019-04-22
The Aronszajn-Donoghue theorem provides a good understanding of the subtle theory of rank one perturbations. One of their statements consists of the mutual singularity of the singular parts of the spectral measures under rank one perturbations. For higher rank perturbations, simple examples show that the singular parts can behave more complicatedly. Nonetheless, a 'vector' version of the mutual singularity of the singular parts and a modified Aleksandrov spectral averaging prevail in the finite rank setting. Applications of these results yield further restrictions of the singular spectrum under finite rank perturbations. The presentation is based on joint work with Sergei Treil.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122407&date=2019-04-22String-Math Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125417&date=2019-04-22
3 dimensional \(N=4\) supersymmetric quantum field theories have two distinguished topological twists, called Higgs and Coulomb (though we periodically get confused about which is which). These two twists manifest very interesting mathematical objects in Lie theory and algebraic geometry, which don't seem to obviously be related, except through this bridge in QFT. I'll do my best to explain what physicists know to mathematicians, what mathematicians know to physicists, and if I fail at both, hopefully there will be some comedy value in my attempt.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125417&date=2019-04-22Arithmetic Geometry and Number Theory RTG Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125423&date=2019-04-22
Wan conjectured that the variation of zeta functions along towers of curves associated to the $p$-adic etale cohomology of a fibration of smooth proper ordinary varieties should satisfy several stabilizing properties. The most basic of these conjectures state that the genera of the curves in these towers grow in a regular way. We state and prove a generalization of this conjecture, which applies to the graded pieces of the slope filtration of an overconvergent $F$-isocrystal.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125423&date=2019-04-22Differential Geometry Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124853&date=2019-04-22
We will discuss Witten’s gauge theory approach to Jones polynomial by counting solutions to the Kapustin-Witten(KW) equations with singular boundary conditions over 4-manifolds. We will give a classification of solutions to the KW equations on $S^1\times\Sigma\times \mathbb R^+$ with $\Sigma$ a Riemann surface. We prove that all solutions to the KW equations over $S^1\times\Sigma\times \mathbb R^+$ are $S^1$ direction invariant and we give a classification of the KW monopole over $\Sigma\times R^+$ based on the Hermitian-Yang-Mills type structure of KW monopole equation. This is based on joint works with Rafe Mazzeo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124853&date=2019-04-22Tarski Lecture, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125070&date=2019-04-22
The Kepler Conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space can have density greater than that of the face-centered cubic packing. This talk will describe the history and proof of the conjecture, including early attempts to reduce the problem to a finite calculation, controversy surrounding claimed proofs, the announcement of a proof by Sam Ferguson and me more than 20 years ago, and finally a formal proof of the Kepler conjecture in the HOL Light proof assistant in 2014.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125070&date=2019-04-22Analysis and PDE Seminar, Apr 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125223&date=2019-04-22
I will present a theorem on the full finite codimension asymptotic stability of the Schwarzschild family of black holes. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125223&date=2019-04-22Seminar 217, Risk Management: CANCELLED, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122095&date=2019-04-23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122095&date=2019-04-23Student Harmonic Analysis and PDE Seminar (HADES), Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125388&date=2019-04-23
Multiphase mean curvature flow has, due to its importance in materials science, received a lot of attention over the last decades. On the one hand, there is substantial recent progress in the construction of weak solutions. On the other hand, strong solutions are—in particular in the planar case of networks—very well understood.<br />
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In this talk, after giving an overview of the topic, I will present a weak-strong uniqueness principle for multiphase mean curvature flow: as long as a strong solution to multiphase mean curvature flow exists, any distributional solution with optimal energy dissipation rate has to coincide with this solution.<br />
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In our proof we construct a suitable relative entropy functional, which in this geometric context may be viewed as a time-dependent variant of calibrations. Just like the existence of a calibration guarantees that one has found a global minimum, the existence of a “time-dependent calibration” ensures that the route of steepest descent in the energy landscape is unique and stable.<br />
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For the purpose of this talk, I will focus on two instructive model cases: a single smooth interface and a single triple junction.<br />
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This is a joint work (in progress) with Julian Fischer, Sebastian Hensel, and Thilo Simon.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125388&date=2019-04-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125420&date=2019-04-23
Why do we have the version of Galois theory that we do – why, indeed, do we have Galois theory at all? This talk traces conflicting 19th-century visions of what it would be to solve, or better to understand, polynomial equations and finds the forgotten role of Felix Klein in promoting Galois's ideas in Germany and America.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125420&date=2019-04-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Apr 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125421&date=2019-04-23
This is a background talk on problems about indecomposable rank two bundles on Pn. We pay special attention to those that are limits of split bundles.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125421&date=2019-04-23Topology Seminar (Introductory Talk), Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125315&date=2019-04-24
I will describe Khovanov's categorification of the Jones polynomial. We will talk about some applications of Khovanov homology to low-dimensional topology, such as Rasmussen's proof that the four-ball genus of the \((p,q)\) torus knot is \((p-1)(q-1)/2\). We will also talk about some directions in which the theory has been generalized.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125315&date=2019-04-24The topologies of random real algebraic hypersufaces, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125369&date=2019-04-24
The topology of a hyper-surface in P^n(R) <br />
of high degree can be very complicated .However <br />
if we choose the surface at random there is a universal <br />
law . Little is known about this law and it appears <br />
to be dramatically different for n=2 and n>2 .<br />
There is a similar theory for zero sets of monochromatic <br />
waves which model nodal sets .<br />
Joint work with Y.Canzani and I.Wigmanhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125369&date=2019-04-24Representation Theory and Mathematical Physics Seminar, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125415&date=2019-04-24
I give an introduction to the BV-BFV formalism and discuss the setting of certain AKSZ theories. Moreover, I describe a globalization procedure using concepts of formal geometry, which extends the Quantum Master Equation for manifolds with boundary.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125415&date=2019-04-24Tarski Lecture, Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125071&date=2019-04-24
This talk will describe a broad long-term research program to make formal proofs in mathematics a practical reality. A formal proof is a mathematical proof that has been checked exhaustively by computer, on the basis of the fundamental axioms of mathematics and the primitive inference rules of logic. The field has progressed to the point that it is now possible to give formal proofs of major theorems in mathematics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125071&date=2019-04-24Topology Seminar (Main Talk), Apr 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125316&date=2019-04-24
I will describe a construction of a stable homotopy type which is a knot invariant, and whose (ordinary) homology is Khovanov homology. We will state some applications of this spatial refinement. Time permitting, we will describe further spatial refinements of other variants of Khovanov homology, such as invariants for tangles. This is joint with Robert Lipshitz and Tyler Lawson.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125316&date=2019-04-24Applied Math Seminar, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123969&date=2019-04-25
In this talk, we will present some stochastic algorithms and numerical results for solving electromagnetic problems in nano-particles and random meta-materials. Firstly, we will present a path integral Monte Carlo method for computing magnetic polarizability tensors of nano-particles of complex geometries for material sciences applications. The method relies on a Feynman-Kac formula involving reflecting Brown motions (RBMs) and accurate computation of the local time of the RBMs using a random walk-on-spheres technique. Secondly, in order to optimize functional properties of 3-D random meta-materials (MMs), we will present a stochastic representation scheme for random MMs with volume exclusion constrains and given correlations, a fast volume integral equation electromagnetic solver for the scattering of a large number of meta-atoms of typical geometric shapes (cubes, spheres, and ellipses) in layered media, and a procedure to optimize the optical properties of the MMs. A new fast multipole method for 3-D Helmholtz equation for layered media will be presented based on new multipole expansion (ME) and multipole to local translation (M2L) operators for layered media Green's functions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123969&date=2019-04-25Cooperating with the Curse of Dimensionality, Apr 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125386&date=2019-04-25
The curse of dimensionality arises when analyzing high-dimensional data and non-Euclidean data, such as network data, which are ubiquitous nowadays. It causes counter-intuitive phenomena and makes traditional statistical tools less effective or inapplicable. On the other hand, some counter-intuitive phenomena might be explained by some universal patterns, which could be used to form new effective tools in dealing with high-dimensional/non-Euclidean data. In this talk, one such unique pattern is explored and applied to fundamental statistical tasks, including hypothesis testing and cluster analysis, leading to substantial improvements in conducting these tasks for high-dimensional/non-Euclidean data. Some other related topics will also be briefly discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125386&date=2019-04-25Student Probability/PDE Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125045&date=2019-04-26
We revisit the [R. Jordan, D. Kinderlehrer, and F. Otto. The variational formulation of the Fokker-Planck equation (1998)] variational characterization of diffusion as entropic gradient flux, and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in terms of the quadratic Wasserstein metric. We obtain novel, stochastic-process versions of these features, valid along almost every trajectory of the diffusive motion in both the forward and, most transparently, the backward, directions of time, using a very direct perturbation analysis; the original results follow then simply by taking expectations. As a bonus, we derive the Cordero-Erausquin version of the so-called HWI inequality relating relative entropy, Fisher information and Wasserstein distance.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125045&date=2019-04-26Representation Theory and Mathematical Physics Seminar, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125068&date=2019-04-26
Hurwitz numbers enumerate branched coverings of the Riemann sphere with specified branching profiles. \(\tau \)-functions of hypergeometric type for the KP and \(2D\)-Toda integrable hierarchies serve as combinatorial generating functions for weighted sums over Hurwitz numbers, with weights chosen as symmetric functions of a set of auxiliary parameters determined by a weight generating function. This talk will explain how multicurrent correlators may be used to explicitly generate weighted Hurwitz numbers as weighted polyonomials in the Taylor coefficients of the weight generating function, without any knowledge required either of symmetric group characters or the Kostka matrices relating different bases of the ring of symmetric functions. The case of rational weight generating functions will be the main illustrative example.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125068&date=2019-04-26Tarski Lecture, Apr 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125072&date=2019-04-26
In 1995, Kontsevich introduced a new form of integration, call motivic integration. From the start, the development of motivic integration has been guided by model theory, especially quantifier elimination. One particularly useful result has been a far-reaching generalization of the Ax-Kochen-Ersov transfer principle in logic to integration. This talk will give a gentle introduction to motivic integration and will highlight some applications to the Langlands program.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125072&date=2019-04-26Combinatorics Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125373&date=2019-04-29
The branching rule for representations of the symmetric group tells us that, over a field of characteristic zero, the dimension of the irreducible representation indexed by a partition λ is given by the number of directed lattice paths from λ (though of as an integer vector) to the origin that stay inside the dominant Weyl chamber. Over a field of positive characteristic (or for Hecke algebras at roots of unity) this is no longer true, and the dimension of an irreducible is in general unknown. We will see, however, that there is a nice class of irreducibles (called calibrated, completely splittable or tame by different authors) whose dimension is given by the number of lattice paths to the origin that stay within a dilation of the fundamental alcove. Then we will provide an explicit resolution of these modules by Specht modules, whose dimensions are as in the characteristic zero case. This gives a representation-theoretic interpretation of combinatorial results of Filasetta, Krattenthaler and others. Based on joint work with C. Bowman and E. Norton.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125373&date=2019-04-29Berkeley Statistics and Machine Learning Forum, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124352&date=2019-04-29
Full details about this meeting will be posted here: https://www.benty-fields.com/manage_jc?groupid=191. <br />
<br />
The Berkeley Statistics and Machine Learning Forum meets weekly to discuss current applications across a wide variety of research domains and software methodologies. Register here to view, propose and vote for this group's upcoming discussion topics. All interested members of the UC Berkeley and LBL communities are welcome and encouraged to attend. Questions may be directed to François Lanusse.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124352&date=2019-04-29Probabilistic Operator Algebra Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124949&date=2019-04-29
In this talk I will discuss the process of “unbounding” a topology on a vector lattice. In the $L_p$-space case this process converts the norm topology to the topology of convergence in measure . I will then discuss how unbounded topologies connect with the minimal and universal objects in the category of vector lattices, and how some of their natural properties cannot be characterized in ZFC.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124949&date=2019-04-29String-Math Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125418&date=2019-04-29
Both the Higgs bundle moduli space and the moduli space of flat connections have a natural stratification induced by a \(C^*\)-action. In both of these stratifications, each stratum is a holomorphic fibration over a connected component of complex variations of Hodge structure. While the nonabelian Hodge correspondence provides a homeomorphism between Higgs bundles and flat connections, this homeomorphism does not preserve the respective strata. The closed stratum on the Higgs bundle side is the image of the Hitchin section and the closed stratum in the space of flat connections is the space of opers. In this talk, we will show how many of the relationships between opers and the Hitchin section extend to general strata. In particular, we will show that the conformal limit identifies certain holomorphic Lagrangian subspaces of the stratifications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125418&date=2019-04-29Analysis and PDE Seminar, Apr 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125374&date=2019-04-29
A fundamental problem in the context of Einstein’s equations of general relativity is to understand the dynamical evolution of small perturbations of stationary black hole solutions. It is expected that there is a discrete set of characteristic frequencies that play a dominant role at late times and carry information about the nature of the black hole, much like how the normal frequencies of a vibrating guitar string play an important role in the resulting sound wave. These frequencies are called quasinormal frequencies or resonant frequencies and they are closely related to scattering resonances in the study of Schrödinger-type equations. I will consider the linear wave equation on black hole backgrounds as a toy model for Einstein’s equations and give an introduction to resonances in this setting. Then I will discuss a new method of defining and studying resonances on asymptotically flat spacetimes, developed from joint work with Claude Warnick, which puts resonances on the same footing as normal modes by showing that they are eigenfunctions of a natural operator acting on a Hilbert space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=125374&date=2019-04-29Seminar 217, Risk Management: The Implication of Information Network in Market Quality and Market Reaction to Public Announcements, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122097&date=2019-04-30
This research studies the role of information network in market quality and market reaction to public announcements. We propose in this article a three-period rational noisy expected equilibrium model by taking both public and private information into account with an embedded information network structure among market traders. Closed form expressions for market reaction and market quality are derived as a function of topological structure of the network and several novel results are revealed. The trading volume and price change have different responses to network connectedness. As network connectedness increases, there is a downward trend for price change. The downward trend are decreasing which reﬂects that the market eﬃciency can not increase to inﬁnite in reality. However, the change of trading volume is uncertain because it depends on two attributes of the network, the uniformity and connectedness, it is hard to compare which one dominate another one. To the market quality, the information precision can increase market liquidity, market eﬃciency and decrease the cost of capital, network connectedness plays the same role in market eﬃciency and cost of capital, while it has a non-monotone inﬂuence towards market liquidity. And also network will suppress the eﬀect caused by disclosure.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122097&date=2019-04-30Representation Theory and Mathematical Physics Seminar, Apr 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124749&date=2019-04-30
The algebra of charged free fermions participates in the construction of classical boson-fermion correspondence and provides vertex operator realization of Schur symmetric functions. We will show how vertex operator realizations of several other famous families of symmetric functions (Hall-Littlewood polynomials, shifted Schur functions, multiparameter Schur Q-functions) can be obtained by simple modifications of operators of charged free fermions and make some notes on the corresponding versions of boson-fermion correspondence.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=124749&date=2019-04-30