• Speaker: Luis Silvestre, University of Chicago
• Title: Integro-differential diffusion and the Boltzmann equation
• Date: 01/26/2021
• Time: 4:30 PM - 5:30 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin (levina@msu.edu)

Integro-differential 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.

• Speaker: Jordan Ellenberg, University of Wisconsin–Madison
• Title: Beyond rank
• Date: 02/09/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: 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 well-understood, 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 to-be-specified proper subset of these topics, and am happy to chat afterwards about the others.

• Speaker: Andrea Nahmod, University of Massachusetts Amherst
• Title: Propagation of randomness under the flow of nonlinear dispersive equations
• Date: 03/09/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: 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.

• Speaker: CRLT Players , https://crlt.umich.edu/crltplayers
• Title: Shoulda, Woulda, Coulda: Moving Beyond Failure and Actively Cultivating a More Equitable Academy
• Date: 03/30/2021
• Time: 4:00 PM - 5:30 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

The University of Michigan Math Department is hosting a special colloquium on Tuesday, March 30, 4pm-5:30pm. 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, post-docs, 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). Pre-registration 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 systems--as administrators, instructors, or learners--they 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 man’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.

• Speaker: Adrian Ioana, UC San Diego
• Title: Classification and rigidity for group von Neumann algebras
• Date: 04/13/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: 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.