# Difference between revisions of "Colloquia/Fall18"

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# Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

## Fall 2013

date speaker title host(s)
Sept 6 Matt Baker (Georgia Institute of Technology) Riemann-Roch for Graphs and Applications Ellenberg
Sept 13 Uri Andrews (University of Wisconsin) A hop, skip, and a jump through the degrees of relative provability
Sept 20 Valerio Toledano Laredo (Northeastern) Flat connections and quantum groups Gurevich
Wed, Sept 25, 2:30PM in B139 Ayelet Lindenstrauss (Indiana University) Taylor Series in Homotopy Theory Meyer
Wed, Sept 25 (LAA lecture) Jim Demmel (Berkeley) Communication-Avoiding Algorithms for Linear Algebra and Beyond Gurevich
Thurs, Sept 26 (LAA lecture, Joint with Applied Algebra Seminar) Jim Demmel (Berkeley) Implementing Communication-Avoiding Algorithms Gurevich
Sept 27 (LAA lecture) Jim Demmel (Berkeley) Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays Gurevich
Oct 4 Frank Sottile (Texas A&M) Galois groups of Schubert problems Caldararu
Oct 11 Amie Wilkinson (Chicago) Robust mechanisms for chaos WIMAW (Cladek)
Tues, Oct 15, 4PM (Distinguished Lecture) Alexei Borodin (MIT) Integrable probability I Valko
Wed, Oct 16, 2:30PM (Distinguished Lecture) Alexei Borodin (MIT) Integrable probability II Valko
Oct 18 No colloquium due to the distinguished lecture
Oct 25 Paul Garrett (Minnesota) Boundary-value problems, generalized functions, and zeros of zeta functions Gurevich
Nov 1 Allison Lewko (Columbia University) On sets of large doubling, Lambda(4) sets, and error-correcting codes Stovall
Nov 8 Tim Riley (Cornell) Hydra groups Dymarz
Nov 15 and later Reserved Street
Nov 22 Tianling Jin (University of Chicago) Solutions of some Monge-Ampere equations with degeneracy or singularities. Bolotin
Mon, Nov 25, 4PM Lin Lin (Lawrence Berkeley National Lab) Fast algorithms for electronic structure analysis Jin
Tue, Nov 26, 4PM, B139 Clinton Conley (Cornell) Descriptive set-theoretic graph theory Lempp
Mon, Dec 2, 4PM Simon Marshall (Northwestern) Semiclassical estimates for eigenfunctions on locally symmetric spaces Denissov
Wed, Dec 4, 4PM Steven Sam (Berkeley) Free Resolutions and Symmetry Boston
Fri, Dec 6 Paul Hand (MIT) Simplifications of the lifting approach for quadratic signal recovery problems Thiffeault
Fri, Dec. 6 and Sat Dec. 7 Conference in honor of Dick Askey
Mon, Dec. 9, 4pm, VV B239 Jacob Bedrossian (Courant Institute) Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations Bolotin
Wed, Dec 11, 4PM Lu Wang (Johns Hopkins) Rigidity of Self-shrinkers of Mean Curvature Flow Viaclovsky
Fri, Dec. 13, 2:25pm, VV 901 Chanwoo Kim (Cambridge) Regularity of the Boltzmann equation in convex domains Bolotin
Tues, Dec 17, 4PM Perla Sousi (Cambridge) The effect of drift on the volume of the Wiener sausage Seppalainen
Wed, Dec 18, 4PM Dustin Cartwright (Yale) Tropical Complexes Gurevich

## Spring 2014

date speaker title host(s)
Mon, Jan 6, 4PM Aaron Lauda (USC) An introduction to diagrammatic categorification Caldararu
Wed, Jan 8, 4PM Karin Melnick (Maryland) Normal forms for local flows on parabolic geometries Kent
Jan 10, 4PM Yen Do (Yale) Convergence of Fourier series and multilinear analysis Denissov
Mon, Jan 13, 4pm Yi Wang (Stanford) Isoperimetric Inequality and Q-curvature Viaclovsky
Wen, Jan 15, 4pm Wei Xiang (University of Oxford) Conservation Laws and Shock Waves Bolotin
Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations Thiffeault
Thu, Jan 23, 2:25, VV901 Mykhaylo Shkolnikov (Berkeley) Intertwinings, wave equations and growth models Seppalainen
Jan 24 Yaniv Plan (Michigan) Low-dimensionality in mathematical signal processing Thiffeault
Jan 31 Urbashi Mitra (USC) Underwater Networks: A Convergence of Communications, Control and Sensing Gurevich
Feb 7 David Treumann (Boston College) Functoriality, Smith theory, and the Brauer homomorphism Street
Feb 14 Alexander Karp (Columbia Teacher's College) History of Mathematics Education as a Research Field and as Magistra Vitae Kiselev
Feb 21 Svetlana Jitomirskaya (UC-Irvine) Analytic quasiperiodic cocycles Kiselev
Feb 28 Michael Shelley (Courant) Spagnolie
March 7 Steve Zelditch (Northwestern) Seeger
March 14
March 21 Spring Break No Colloquium
March 28 Michael Lacey (GA Tech) The Two Weight Inequality for the Hilbert Transform Street
April 4 Richard Schwartz (Brown) Mari-Beffa
April 11 Risi Kondor (Chicago) Gurevich
April 18 (Wasow Lecture) Christopher Sogge (Johns Hopkins) Seeger
April 25 Charles Doran(University of Alberta) Song
Monday, April 28 (Distinguished Lecture) David Eisenbud(Berkeley) A mystery concerning algebraic plane curves Maxim
Tuesday, April 29 (Distinguished Lecture) David Eisenbud(Berkeley) Matrix factorizations old and new Maxim
Wednesday, April 30 (Distinguished Lecture) David Eisenbud(Berkeley) Easy solution of polynomial equations over finite fields Maxim
May 2 Lek-Heng Lim (Chicago) Boston
May 9 Rachel Ward (UT Austin) WIMAW

## Abstracts

### January 6: Aaron Lauda (USC)

An introduction to diagrammatic categorification

Categorification seeks to reveal a hidden layer in mathematical structures. Often the resulting structures can be combinatorially complex objects making them difficult to study. One method of overcoming this difficulty, that has proven very successful, is to encode the categorification into a diagrammatic calculus that makes computations simple and intuitive.

In this talk I will review some of the original considerations that led to the categorification philosophy. We will examine how the diagrammatic perspective has helped to produce new categorifications having profound applications to algebra, representation theory, and low-dimensional topology.

### January 8: Karin Melnick (Maryland)

Normal forms for local flows on parabolic geometries

The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.

### January 10, 4PM: Yen Do (Yale)

Convergence of Fourier series and multilinear analysis

Almost everywhere convergence of the Fourier series of square integrable functions was first proved by Lennart Carleson in 1966, and the proof has lead to deep developments in various multilinear settings. In this talk I would like to introduce a brief history of the subject and sketch some recent developments, some of these involve my joint works with collaborators.

### Mon, January 13: Yi Wang (Stanford)

Isoperimetric Inequality and Q-curvature

A well-known question in differential geometry is to prove the isoperimetric inequality under intrinsic curvature conditions. In dimension 2, the isoperimetric inequality is controlled by the integral of the positive part of the Gaussian curvature. In my recent work, I prove that on simply connected conformally flat manifolds of higher dimensions, the role of the Gaussian curvature can be replaced by the Branson's Q-curvature. The isoperimetric inequality is valid if the integral of the Q-curvature is below a sharp threshold. Moreover, the isoperimetric constant depends only on the integrals of the Q-curvature. The proof relies on the theory of $A_p$ weights in harmonic analysis.

### January 15: Wei Xiang (University of Oxford)

Conservation Laws and Shock Waves

The study of continuum physics gave birth to the theory of quasilinear systems in divergence form, commonly called conservation laws. In this talk, conservation laws, the Euler equations, and the definition of the corresponding weak solutions will be introduced first. Then a short history of the studying of conservation laws and shock waves will be given. Finally I would like to present two of our current research projects. One is on the mathematical analysis of shock diffraction by convex cornered wedges, and the other one is on the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws.

Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations

### Fri, Jan 17: Adrianna Gillman (Dartmouth)

Fast direct solvers for linear partial differential equations

The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional right-hand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.

### Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley)

Intertwinings, wave equations and growth models

We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal.

### Jan 24: Yaniv Plan (Michigan)

Low-dimensionality in mathematical signal processing

Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information -- in other words, low dimensionality of the signal -- is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of low-dimensionality and measurement acquisition.

### Thur, Jan 30: Urbashi Mitra (USC)

Underwater Networks: A Convergence of Communications, Control and Sensing

The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and water-related applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multi-path, time-variation and range-dependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.

### Feb 7: David Treumann (Boston College)

Functoriality, Smith theory, and the Brauer homomorphism

Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p. I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p. This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of L-groups on the Galois side. The talk is based on joint work with Akshay Venkatesh. I hope understanding the talk will require less number theory background than understanding the abstract.

### Feb 14: Alexander Karp (Columbia Teacher's College)

History of Mathematics Education as a Research Field and as Magistra Vitae

The presentation will be based on the experience of putting together and editing the Handbook on the History of Mathematics Education, which will be published by Springer in the near future. This volume, which was prepared by a large group of researchers from different countries, contains the first systematic account of the history of the development of mathematics education in the whole world (and not just in some particular country or region). The editing of such a book gave rise to thoughts about the methodology of research in this field, and also about what constitutes an object of such research. These are the thoughts that the presenter intends to share with his audience. From them, it is natural to pass to an analysis of the current situation and how it might develop.

### Feb 21: Svetlana Jitomirskaya (UC-Irvine)

Analytic quasiperiodic cocycles

Analytic quasiperiodic matrix cocycles is a simple dynamical system, where analytic and dynamical properties are related in an unexpected and remarkable way. We will focus on this relation, leading to a new approach to the proof of joint continuity of Lyapunov exponents in frequency and cocycle, at irrational frequency, first proved for SL(2,C) cocycles in Bourgain-Jitom., 2002. The approach is powerful enough to handle singular and multidimensional cocycles, thus establishing the above continuity in full generality. This has important consequences including a dense open version of Bochi-Viana theorem in this setting, with a completely different underlying mechanism of the proof. A large part of the talk is a report on a joint work with A. Avila and C. Sadel.

### March 28: Michael Lacey (GA Tech)

The Two Weight Inequality for the Hilbert Transform

The individual two weight inequality for the Hilbert transform asks for a real variable characterization of those pairs of weights (u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). This question arises naturally in different settings, most famously in work of Sarason. Answering in the positive a deep conjecture of Nazarov-Treil-Volberg, the mapping property of the Hilbert transform is characterized by a triple of conditions, the first being a two-weight Poisson A2 on the pair of weights, with a pair of so-called testing inequalities, uniform over all intervals. This is the first result of this type for a singular integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)