• Speaker: Nicole Louie, University of Wisconsin-Madison; Chundou, University of Wisconsin-Madison
• Title: Building Racial Justice in Mathematics Education: A Seat at the Breakfast Table
• Date: 02/27/2023
• Time: 2:00 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Lisa Keller (kellerl@msu.edu)

Everyone seems to be talking about racial equity and justice these days. Increasingly, scholars in mathematics education are recognizing the need to center the voices of those most affected—i.e., Black, Latine, Asian, and Indigenous children and families—in these discussions. Our current project explores participatory design research (PDR) as a tool for building school, university, student, and parent capacity for centering children of color and their families as researchers and designers of middle school mathematics learning, in a small but diverse Midwestern city. In this talk, we will discuss the challenges we are experiencing and what we are learning about PDR, racial justice, and ourselves, as we work to bring youth of color to the table with us to eat, learn, and act together. Join Zoom Meeting: https://msu.zoom.us/j/94209936218 Passcode: PRIME

• Speaker: Chamila Malagoda Gamage, MSU
• Title: Capacity Constrained Barycenter Problem and its Duality
• Date: 02/27/2023
• Time: 2:00 PM - 3:00 PM
• Place: C329 Wells Hall (Virtual Meeting Link)
• Contact: Craig Gross (grosscra@msu.edu)

The problem of finding a barycenter in the Wasserstein space is a nonlinear interpolation between several probability measures. In this talk we will discuss the notion of barycenters in the Wasserstein space under a capacity constraint on the mass transported and its dual formulation. $\\$ This will be a hybrid seminar and take place in C329 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

• Speaker: Michail Savvas, University of Texas
• Title: Stabilizer reduction for derived stacks
• Date: 02/27/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Francois Greer (greerfra@msu.edu)

Suppose that a group acts on a variety. When can the variety and the action be resolved so that all stabilizers are finite? Kirwan gave an answer to this question in the 1980s through an explicit blowup algorithm for smooth varieties with group actions in the context of Geometric Invariant Theory (GIT). In this talk, we will explain how to generalize Kirwan's algorithm to Artin stacks in derived algebraic geometry, which, in particular, include classical, potentially singular, quotient stacks that arise from group actions in GIT. Based on joint work with Jeroen Hekking and David Rydh.

• Speaker: Brent Nelson, MSU
• Title: Combinatorics of free probability
• Date: 02/27/2023
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

The lattice of non-crossing partitions plays an important role in the theory of free probability. In particular, it allows one to define the so-called free cumulants, which capture the same information as a non-commutative distribution. In this talk I will provide an introduction to these ideas and show how cumulants offer a characterization of free independence as well as an easy proof of the free central limit theorem.

• Speaker: Francis Bonahon, MSU
• Title: The quantum trace for skein algebras of surfaces (continued)
• Date: 02/27/2023
• Time: 4:00 PM - 4:30 PM
• Place: C204A Wells Hall
• Contact: Michael Shapiro (mshapiro@msu.edu)

I will discuss the technical details of the construction of the quantum trace homomorphism, going from the SL_2-skein algebra to the quantum Teichmüller space of Chekhov-Fock.

• Speaker: Ryan Stees, Indiana University
• Title: Milnor's invariants for knots and links in closed orientable 3-manifolds
• Date: 02/28/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

Early in his career, John Milnor defined his seminal link invariants, now called Milnor's $\overline{\mu}$-invariants. They are topological concordance invariants of links in $S^3$, and much is known about them. However, until recently, few results have extended Milnor's work to links in other closed orientable 3-manifolds, and such extensions have done so for special classes of 3-manifolds or specific types of links. In this talk, I will discuss an extension of these invariants to concordance invariants of knots and links in any closed orientable 3-manifold, discuss some theorems that justify calling them ``Milnor's invariants", and study their properties.

• Speaker: Andrei Prokhorov, University of Michigan
• Title: Probabilistic approach to Zamolodchikov conjecture for one point conformal blocks on the torus
• Date: 03/01/2023
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall
• Contact: Konstantin Matetski (matetski@msu.edu)

Liouville field theory is the model for two-dimensional quantum gravity. It was constructed rigorously using probabilistic methods by David-Kupiainen-Rhodes-Vargas in 2016. According to the conformal bootstrap conjecture n-point correlation functions can be expressed in terms of 3-point correlation functions and so-called conformal blocks. We restrict ourselves to the case of one point correlation function of the Liouville field theory on the torus. We want to study conformal blocks. They are described using complicated asymptotic series. The probabilistic model for them was suggested by Ghosal-Remy-Sun-Sun in 2021. It allowed showing that the asymptotic series is actually converging in a small disc. Liouville field theory has central charge c associated to it. Zamolodchikov in 1984 conjectured that conformal blocks have a limit as c goes to infinity. The limit was called classical conformal blocks. We use the probabilistic formula for conformal blocks to prove Zamolodchikov conjecture and show that the asymptotic series for them is converging in a small disc. This is joint work with Harini Desiraju and Promit Ghosal.

• Speaker: Sophie Spirkl, University of Waterloo
• Title: The Kromatic Symmetric Function
• Date: 03/01/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

The chromatic symmetric function, introduced by Stanley, counts graph colourings, recording the number of vertices of each colour. I will talk about a K-theoretic analogue of the chromatic symmetric function, in which we are colouring each vertex with a set of colours (rather than a single colour), as well as some results and open questions for this new function. Joint work with Logan Crew and Oliver Pechenik.

• Speaker: Igor Rapinchuk, MSU
• Title: Profinite groups and infinite Galois theory
• Date: 03/01/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: Zhongshan An, U. Mich
• Title: Quasi-local Hamiltonians for compact initial data sets
• Date: 03/01/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

In general relativity, one of the most interesting ways to construct notions of energy is the method of Hamiltonian analysis. For asymptotically flat spacetimes, this approach yields the well-known ADM mass. In order to define quasi-local energy/mass for compact initial data sets, one would like to apply the Hamiltonian analysis of GR on compact spacetimes with time-like boundary. Traditionally, this has been done based on fixing the Dirichlet boundary condition of the spacetimes — one of the most well-known work along this thread is the Brown-York quasi-local mass. In this talk we will discuss in detail the relation between the study of initial boundary value problem for vacuum Einstein equations and the Hamiltonian analysis on compact spacetimes. Then we will construct a notion of quasi-local Hamiltonian (energy) based on a well-posed initial boundary value problem.

• Speaker: Jie Yang, MSU
• Title: Everywhere convergent formal series
• Date: 03/02/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Jie Yang (yangji79@msu.edu)

No abstract available.

• Speaker: Yuejie Chi, Carnegie Mellon University
• Title: ZOOM TALK (password the smallest prime > 100) - The Non-asymptotics of Reinforcement Learning
• Date: 03/02/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen ()

Reinforcement learning (RL) is garnering significant interest in recent years due to its success in a wide variety of modern applications. However, theoretical understandings on the non-asymptotic sample and computational efficiencies of RL algorithms remain elusive, and are in imminent need to cope with the ever-increasing problem dimensions. In this talk, we discuss our recent progress that sheds light on understanding the efficacy of popular RL algorithms in finding the optimal policy in tabular Markov decision processes.

• Speaker: Huyi Hu, Michigan State University
• Title:  Quasi-stability for partially hyperbolic diffeomorphisms
• Date: 03/02/2023
• Time: 3:00 PM - 4:00 PM
• Place: A126 Wells Hall
• Contact: Huyi Hu (hhu@msu.edu)

The motivation of the work is to study topological properties of partially hyperbolic systems which are similar to those of uniformly hyperbolic systems. We try to obtain some properties similar to these of uniformly hyperbolic systems by ``ignoring'' the motions along the center direction. We show that any partially hyperbolic systems are quasi-stable in the sense that for any homeomorphism $g$ $C^0$-close to $f$, there exist a continuous map $\pi$ from $M$ to itself and a family of locally defined continuous maps $\{\tau_x\}$, which send points along the center direction, such that $$\pi\circ g=\tau_{fx}\circ f\circ\pi. $$ In particular, if $f$ has $C^1$ center foliation, then we can make the motion $\tau$ along the center foliation. As application we obtain some continuity properties for topological entropy.

• Speaker: Katy Craig, UCSB
• Title: Optimal Transport in Machine Learning and Partial Differential Equations
• Date: 03/02/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Olga Turanova (turanova@msu.edu)

Over the past ten years, optimal transport has become a fundamental tool in statistics and machine learning: the 2-Wasserstein metric provides a new notion of distance for classifying distributions and a rich geometry for interpolating between them. In parallel, optimal transport has gained mathematical significance by providing new tools for studying stability and limiting behavior of partial differential equations, through the theory of 2-Wasserstein gradient flows. In fact, the success optimal transport in each of these contexts ultimately relies on the same fundamental property of the 2-Wasserstein metric: as originally discovered by Otto, the 2-Wasserstein metric is unique among classical optimal transport metrics in that it has a formal Riemannian structure. In my talk, I will introduce the theory of optimal transport, explain the special geometric structure of the 2-Wasserstein metric, and illustrate the essential role it plays in how optimal transport is used in both machine learning and partial differential equations.