• Speaker: Leonid Chekhov, Michigan State University
• Title: Symplectic groupoid and cluster algebra description of closed Riemann surfaces
• Date: 09/12/2022
• Time: 12:30 PM - 1:30 PM
• Place: C304 Wells Hall
• Contact: Linhui Shen (shenlin1@msu.edu)

We use the Fock-Goncharov higher Teichmuller space directed networks to solve the symplectic groupoid condition: parameterize pairs of $SL_n$ matrices (B,A) with A unipotent such that $BAB^T$ is also unipotent. A natural Lie-Poisson bracket on B generates the Goldman bracket on elements of A and $BAB^T$, which are simultaneously elements of the corresponding upper cluster algebras. Using this input we identify the space of X-cluster algebra elements with Teichmuller spaces of closed Riemann surfaces of genus 2 (for $n$=3) and 3 (for $n$=4) endowed with Goldman bracket structure: for $g$=2 all geodesic functions are positive Laurent polynomials and Dehn twists correspond to mutations in the corresponding quivers. This is the work in progress with Misha Shapiro.

• Speaker: Brent Nelson, MSU
• Title: Making Weight
• Date: 09/12/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

A weight on a von Neumann algebra is a positive linear map that is permitted to be infinitely valued. It is a generalization of a positive linear functional that arises naturally in the context of crossed products by non-discrete groups, and they are vital to the study of purely infinite von Neumann algebras. In this talk I will provide an introduction to the theory of weights that assumes only the definition of a von Neumann algebra.

• Speaker: Lara Ismert, Embry–Riddle Aeronautical University
• Title: A Liouville-esque theorem for a weakly-defined derivation on B(H)
• Date: 09/13/2022
• Time: 11:00 AM - 11:50 AM
• Place: C304 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

Liouville’s Theorem states that any bounded entire function on the complex plane is necessarily constant. In this talk, we discuss an analogous theorem for a weakly-defined derivation on B(H) studied in recent years by Erik Christensen. As a consequence, we provide new sufficient conditions for when two operators which satisfy the Heisenberg Commutation Relation must both be unbounded.

• Speaker: Brendon Rhoades, UCSD
• Title: Superspace, Vandermondes, and representations
• Date: 09/14/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

We present an extension of the Vandermonde determinant from the polynomial ring to superspace. These superspace Vandermondes are used to construct modules over the symmetric group with (occasionally conjectural) connections to geometry and coinvariant theory. Joint with Andy Wilson.

• Speaker: Jie Yang, MSU
• Title: Organizing meeting for Student Number Theory Seminar
• Date: 09/15/2022
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Jie Yang (yangji79@msu.edu)

In this first meeting, I'll give some motivations towards the study of p-adic modular forms, and explain some central concepts in "eigenvarieties machine" introduced by K. Buzzard. In the end, we will discuss the plan for this seminar.

• Speaker: Jenny Wilson, University of Michigan
• Title: Stability patterns in configuration spaces
• Date: 09/15/2022
• Time: 4:10 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

This talk will give an introduction of the recent field of 'representation stability'. I will discuss how we can use representation theory to illuminate the structure of certain families of groups or topological spaces with actions of the symmetric groups, focusing on configuration spaces as an illustrative example.

• Speaker: Anna Veselovska, Department of Mathematics, Technical University of Munich, Germany
• Title: Super-Resolution on the Two-Dimensional Unit Sphere
• Date: 09/16/2022
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen (iwenmark@msu.edu)

In this talk, we discuss the problem of recovering an atomic measure on the unit 2-sphere S^2 given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on the space of bounded Borel measures on S^2 as suggested by Y. de Castro & F. Gamboa and E. Candes & C. Fernandez-Granda. We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. We support our theoretical results by various numerical examples related to direct solution of the optimization problem and its discretization. This is a joint work with Frank Filbir and Kristof Schroder.