• Speaker: Aldo Garcia Guinto, MSU
• Title: Free Stein dimension of crossed products by finite groups
• Date: 02/06/2023
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

In this talk, we will discuss a free probabilistic quantity called free Stein dimension and compute it for a crossed product by a finite group. The free Stein dimension is the Murray-von Neumann dimension of a particular subspace of derivations. Charlesworth and Nelson defined this quantity in the hope of finding a von Neumann algebra invariant. While it is still not known to be a von Neumann algebra invariant, it is an invariant for finitely generated unital tracial *-algebras and algebraic methods have been more successful than analytic ones in studying it. Our result continues this trend, and reveals a formula for the free Stein dimension of a crossed product by a finite group that is reminiscint of the Schreier formula for a finite index subgroups of free groups.

• Speaker: Amitesh Datta, Princeton University
• Title: Does the Jones polynomial of a knot detect the unknot? A novel approach via braid group representations and class numbers of number fields.
• Date: 02/07/2023
• Time: 3:30 PM - 4:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

How good of an invariant is the Jones polynomial? The question is closely tied to studying braid group representations since the Jones polynomial can be defined as a (normalized) trace of a braid group representation. In this talk, I will present my work developing a new theory to precisely characterize the entries of classical braid group representations, which leads to a generic faithfulness result for the Burau representation of B_4 (the faithfulness is a longstanding question since the 1930s and is equivalent to whether B_4 is a group of 3 x 3 matrices). In forthcoming work, I use this theory to furthermore explicitly characterize the Jones polynomial of all 3-braid closures and generic 4-braid closures. I will also describe my work which uses the class numbers of quadratic number fields to show that the Jones polynomial detects the unknot for 3-braid links - this work also answers (in a strong form) a question of Vaughan Jones. I will discuss all of the relevant background from scratch and illustrate my techniques through simple examples.

• Speaker: Yier Lin, University of Chicago
• Title: Some recent progress in the weak noise theory of the KPZ equation
• Date: 02/08/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Konstantin Matetski (matetski@msu.edu)

In this talk, we will study the Freidlin–Wentzell LDP for the KPZ equation using the variational principle. Such an approach goes under the name of the weak noise theory in physics. We will explain how to extract various limits of the most probable shape of the KPZ equation in the setting of the Freidlin–Wentzell LDP. Some future directions will also be discussed at the end. The talk is based on several joint works with Pierre Yves Gaudreau Lamarre and Li-Cheng Tsai.

• Speaker: Wenjie Fang, Université Gustave Eiffel
• Title: Parabolic Tamari Lattices in Linear Type B
• Date: 02/08/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

We study parabolic aligned elements associated with the type-B Coxeter group and the so-called linear Coxeter element. These elements were introduced algebraically in (Mühle and Williams, 2019) for parabolic quotients of finite Coxeter groups and were characterized by a certain forcing condition on inversions. We focus on the type-B case and give a combinatorial model for these elements in terms of pattern avoidance. Moreover, we describe an equivalence relation on parabolic quotients of the type-B Coxeter group whose equivalence classes are indexed by the aligned elements. We prove that this equivalence relation extends to a congruence relation for the weak order. The resulting quotient lattice is the type-B analogue of the parabolic Tamari lattice introduced for type A in (Mühle and Williams, 2019). These lattices have not appeared in the literature before. As work in progress, we will also talk about various combinatorial models and bijections between them. Joint work with Henri Mühle and Jean-Christophe Novelli.

• Speaker: Igor Rapinchuk, MSU
• Title: Profinite groups and infinite Galois theory
• Date: 02/08/2023
• Time: 3:00 PM - 4:00 PM
• Place: C329 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: Alexander Volberg, MSU
• Title: Noncommutative Bohnenblust--Hille inequalities and application to learning the quantum observables
• Date: 02/08/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

Bohnenblust--Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow sub-exponentially in the degree (Defant—Mastylo—Peres). Such inequalities have found great applications in learning low degree Boolean functions (Eskenazis—Ivanisvili). Motivated by learning quantum observables, a quantum counterpart of Bohnenblust--Hille inequality for Boolean cubes was recently conjectured in Cambyse Rouz\’e, Melchior Wirth, and Haonan Zhang: ``Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions.” arXiv preprint, arXiv:2209.07279, 2022. Haonan Zhang and myself prove such noncommutative Bohnenblust--Hille inequalities with constants that are dimension-free and of exponential growth in the degree. As applications, we study learning problems of quantum observables. (Speaker will present remotely)

• Speaker: Andy Krause, MSU
• Title: AI, ChatGPT, and Teaching
• Date: 02/09/2023
• Time: 11:00 AM - 12:00 PM
• Place: D101 Wells Hall
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Peikai Qi, MSU
• Title: Banach space over Qp
• Date: 02/09/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Elizabeth Munch, MSU
• Title: ZOOM TALK (password the smallest prime > 100) - Combining network analysis and persistent homology for classifying behavior of time series
• Date: 02/09/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen (iwenmark@msu.edu)

Persistent homology, the flagship method of topological data analysis, can be used to provide a quantitative summary of the shape of data. One way to pass data to this method is to start with a finite, discrete metric space (whether or not it arises from a Euclidean embedding) and to study the resulting filtration of the Rips complex. In this talk, we will discuss several available methods for turning a time series into a discrete metric space, including the Takens embedding, $k$-nearest neighbor networks, and ordinal partition networks. Combined with persistent homology and machine learning methods, we show how this can be used to classify behavior in time series in both synthetic and experimental data.

• Speaker: Fan Yang, Michigan State University
• Title: Foliations and transverse invariant measures from a dynamical systems point of view
• Date: 02/09/2023
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall
• Contact: Fan Yang (yangfa31@msu.edu)

In this talk, we will discuss foliations and their transverse invariant measures (i.e., measures on cross-sections that are invariant under the holonomy maps) from a dynamical systems point of view. We will show that for a large family of diffeomorphisms, the unstable foliations admit families of transverse measures that are naturally related to certain probability measures invariant under the dynamics. Given an unstable leaf, we will consider a dynamically defined average that captures its intersection with cross-sections and prove that this averaging will converge exponentially fast to the transverse invariant measures. This is a joint work with Ures, Viana and J. Yang.