Talk_id  Date  Speaker  Title 
26943

Tuesday 1/26 4:30 PM

Luis Silvestre, University of Chicago

Integrodifferential diffusion and the Boltzmann equation
 Luis Silvestre, University of Chicago
 Integrodifferential diffusion and the Boltzmann equation
 01/26/2021
 4:30 PM  5:30 PM
 Online (virtual meeting)
 Aaron D Levin (levina@msu.edu)
Integrodifferential equations have been a very active area of research in the last 20 years. In this talk we will explain what they are and in what sense they are similar to more classical parabolic partial differential equations. We will discuss results on regularity estimates for the Boltzmann equation in this context.

26944

Tuesday 2/2 4:00 PM

Samit Dasgupta, Duke University

Stark's Conjectures and Hilbert's 12th Problem
 Samit Dasgupta, Duke University
 Stark's Conjectures and Hilbert's 12th Problem
 02/02/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory (also known as Hilbert's 12th Problem), and the special values of Lfunctions. The goal of explicit class field theory is to describe the abelian extensions of a ground number field via analytic means intrinsic to the ground field. Meanwhile, there is an abundance of conjectures on the special values of Lfunctions at certain integer points. Of these, Stark's Conjecture has special relevance toward explicit class field theory. I will describe my recent proof, joint with Mahesh Kakde, of the BrumerStark conjecture away from p=2. This conjecture states the existence of certain canonical elements in CM abelian extensions of totally real fields. Next I will describe our proof of an exact formula for these BrumerStark units that had been developed by many authors over the last 15 years. We show that the BrumerStark units along with other elementary quantities generate the maximal abelian extension of totally real number fields, thereby giving a solution to Hilbert's 12th problem for these fields.

26950

Tuesday 2/9 4:00 PM

Jordan Ellenberg, University of Wisconsin–Madison

Beyond rank
 Jordan Ellenberg, University of Wisconsin–Madison
 Beyond rank
 02/09/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The notion of the rank of a matrix is one of the most fundamental in linear algebra. The analogues of this notion in multilinear algebra — e.g., what is the “rank” of an m x n x p array of numbers? — are much less wellunderstood, and are often thought of as of niche interest. At least, that’s how I was brought up to think of them, until Terry Tao explained to me that the resolution of the cap set conjecture by Croot, Lev, Pach, Gijswijt and myself really made use of these ideas! In fact, these notions are of great current interest in a wide range of mathematical subjects at the moment! Issues about “higher rank” arise in complexity theory, data science, geometric combinatorics, additive number theory, quantum mechanics, and commutative algebra — I will manage to say something about some tobespecified proper subset of these topics, and am happy to chat afterwards about the others.

26971

Tuesday 2/16 4:00 PM

Walter Strauss, Brown University

Steady Water Waves
 Walter Strauss, Brown University
 Steady Water Waves
 02/16/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The mathematical study of water waves began with the derivation of the
basic mathematical equations of any fluid by Euler in 1752. Later, water
waves, which have a free boundary at the air interface, played a central role
in the work of Poisson, Cauchy, Stokes, LeviCivita and many others.
In the last quarter century it has become a particularly active mathematical
research area.
I will limit my discussion to classical 2D traveling water waves with vorticity.
By means of local and global bifurcation theory using topological degree,
we now know that there exist many such waves. They are exact smooth
solutions of the Euler equations with the physical boundary conditions.
Numerical computations provide insight into their properties. I will mention
a number of properties that are the subjects of current research such as:
their heights, their steepness, the possibility of selfintersection, and
their stability or instability.

26945

Tuesday 3/9 4:00 PM

Andrea Nahmod, University of Massachusetts Amherst

Propagation of randomness under the flow of nonlinear dispersive equations
 Andrea Nahmod, University of Massachusetts Amherst
 Propagation of randomness under the flow of nonlinear dispersive equations
 03/09/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The study of partial differential equations (PDEs) with randomness has become an important and influential subject in the last few decades. In this talk we focus on the time dynamics of solutions of nonlinear dispersive equations with random initial data. It is well known that in many situations, randomization improves the behavior of solutions to PDEs: the key underlying difficulty is in understanding how randomness propagates under the flow of nonlinear PDEs. In this context, starting with an overview of J. Bourgain's seminal work on the invariance of Gibbs measures for nonlinear Schrödinger equations we describe new methods that offer deeper insights. We discuss in particular the theory of random tensors, a powerful new framework that we developed with Yu Deng and Haitian Yue, which allows us to unravel the propagation of randomness beyond the linear evolution of random data and probe the underlying random structure that lives on high frequencies/fine scales. This enables us to show the existence and uniqueness of solutions to the NLS in an optimal range relative to the probabilistic scaling. A beautiful feature of the solution we find is its explicit expansion in terms of multilinear Gaussians with adapted random tensor coefficients.

26946

Tuesday 3/16 4:00 PM

Martin Olsson, UC Berkeley

The Zariski topology, linear systems, and reconstruction of algebraic varieties
 Martin Olsson, UC Berkeley
 The Zariski topology, linear systems, and reconstruction of algebraic varieties
 03/16/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The classical VeblenYoung theorem characterizes axiomatically projective spaces over fields. It is natural to ask for generalizations of this fundamental result to arbitrary algebraic varieties. In this colloquium I will survey work in this direction, and discuss recent progress characterizing algebraic varieties in terms of their Zariski topological spaces. The main new results are joint with János Kollár, Max Lieblich, and Will Sawin.

29042

Tuesday 3/30 4:00 PM

CRLT Players , https://crlt.umich.edu/crltplayers

Shoulda, Woulda, Coulda: Moving Beyond Failure and Actively Cultivating a More Equitable Academy
 CRLT Players , https://crlt.umich.edu/crltplayers
 Shoulda, Woulda, Coulda: Moving Beyond Failure and Actively Cultivating a More Equitable Academy
 03/30/2021
 4:00 PM  5:30 PM
 Online (virtual meeting)
 Aaron D Levin ()
The University of Michigan Math Department is hosting a special colloquium on Tuesday, March 30, 4pm5:30pm. The CRLT players will present an interactive workshop using a video case study to stimulate reflection on our academic climate and norms. We warmly invite staff, graduate students, postdocs, and faculty from both the UM and MSU Mathematics Departments to attend this unique event. Please note that this workshop is not recommended for undergraduate students. This colloquium is organized by the UM Math Department's Climate Committee and Learning Community for Inclusive Teaching (LCIT). Preregistration is required. Registration Link: https://umich.zoom.us/meeting/register/tJckfu6opjkrH9CMTj5lZzXoHTDyldlT_X_5 Systems of higher education in the U.S. create differential advantage and disadvantage for the people who work and learn in them. When individuals move through these systemsas administrators, instructors, or learnersthey make choices to participate in the perpetuation or the disruption of these inequities. While some perpetuation of inequity can be attributed to ignorance, it is often true that individuals who do understand the harmful impacts of unjust behavior, processes, and structures often fail to address them. This session centers around an embodied case study depicting one manâ€™s meditation on a personal failure and the choices he made afterward that defined his path as an educator. Through session activities, participants will reflect on what failures of this kind indicate about the educational environments in which they occur and how such reflection might prime them to reshape the spaces in which they have responsibilities. In this session, participants will: Reflect on their personal failures to act for justice. Consider how their lived relationship to social inequities within and outside of their educational environment shape their willingness and ability to act. Explore the tension between risk and responsibility when disrupting the status quo. Practice identifying opportunities for proactive justice work in their spheres of influence in the academy. Content flag: The theatrical portion of this session contains strong language. It includes descriptions of sexist, heterosexist, and ableist behaviors and reflection on systemic inequities related to race and socioeconomic status. Note: This colloquium workshop will last 90 minutes, not the typical hour.

26947

Tuesday 4/6 4:00 PM

Emily Riehl, Johns Hopkins University

Elements of ∞Category Theory
 Emily Riehl, Johns Hopkins University
 Elements of ∞Category Theory
 04/06/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
Confusingly for the uninitiated, experts in weak infinitedimensional category theory make use of different definitions of an ∞category, and theorems in the ∞categorical literature are often proven "analytically", in reference to the combinatorial specifications of a particular model. In this talk, we present a new point of view on the foundations of ∞category theory, which allows us to develop the basic theory of ∞categories  adjunctions, limits and colimits, co/cartesian fibrations, and pointwise Kan extensions  "synthetically" starting from axioms that describe an ∞cosmos, the infinitedimensional category in which ∞categories live as objects. We demonstrate that the theorems proven in this manner are "modelindependent", i.e., invariant under change of model. Moreover, there is a formal language with the feature that any statement about ∞categories that is expressible in that language is also invariant under change of model, regardless of whether it is proven through synthetic or analytic techniques. This is joint work with Dominic Verity.

26948

Tuesday 4/13 4:00 PM

Adrian Ioana, UC San Diego

Classification and rigidity for group von Neumann algebras
 Adrian Ioana, UC San Diego
 Classification and rigidity for group von Neumann algebras
 04/13/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
Any countable group G gives rise to a von Neumann algebra L(G). The classification of these group von Neumann algebras is a central theme in operator algebras. I will survey recent rigidity results which provide instances when various algebraic properties of groups, such as the presence or absence of a direct product decomposition, are remembered by their von Neumann algebras. I will also explain the strongest such rigidity results, where L(G) completely remembers G, and discuss some of the open problems in the area.

26949

Tuesday 4/20 4:00 PM

Nicolas Addington, University of Oregon

TBA
 Nicolas Addington, University of Oregon
 TBA
 04/20/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
TBA
