MenuEvents for 04/14/2023 from all calendars
Noncommutative Geometry Seminar
Time: 1:00PM - 2:00PM
Location: ZOOM
Speaker: Haluk Sengun, University of Sheffield
Title: Local theta correspondence via C*-algebras of groups
Abstract: Theta correspondence is a major theme in the theory of automorphic forms and in representation theory. The local version of the correspondence sets up a bijection between certain subsets of admissible duals of suitable pairs of reductive groups. There are two special cases in which the correspondence is known to enjoy extra features, the ‘equal rank’ case where temperedness is preserved and the ‘stable range’ case where unitarity is preserved. In joint work with Bram Mesland (Leiden), we show that in these special cases, the local theta correspondence is actually given by a Morita equivalence of certain C*-algebras. There are interesting applications and some global questions that follow this result. Time permitting, I will discuss some of these.
URL: Event link
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 302
Speaker: Kirill Cherednichenko, University of Bath
Title: Operator-norm homogenisation for Maxwell equations on periodic singular structures
Abstract: I will discuss a new approach to obtaining uniform operator asymptotic estimates in periodic homogenisation. Based on a novel uniform Poincar ́e-type inequality, it bears similarities to the techniques I developed with Cooper (ARMA, 2016) and Velcic (JLMS, 2022).
In the context of the Maxwell system, the analytic framework I will present leads to a new representation for the asymptotics obtained by Birman and Suslina in 2007 for the full system and by Suslina in 2004 for the electric field in the presence of currents. As part of the new asymptotic construction, I will link the leading-order approximation to a family of “homogenised” problems, which was not possible using the earlier method.
The analysis presented applies to a class of inhomogeneous structures modelled by arbitrary periodic Borel measures. However, the results are new even for the particular case of the Lebesgue measure.
This is joint work with Serena D’Onofrio.
Algebra and Combinatorics Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 302
Speaker: Lauren Snider, Texas A&M University
Title: (S_p x S_q)-Invariant G-Parking Functions
Abstract: G-parking functions are generalizations of classical parking functions which depend on a connected multigraph G having a distinct root vertex. Gaydarov and Hopkins classified all such graphs G whose G-parking functions are invariant under action by the symmetric group S_n (where n+1 is the order of G), through which they clarified the relationship between G-parking functions and vector parking functions. In this talk, I will present a classification of all graphs G whose G-parking functions are (S_p x S_q)-invariant, with p+q+1 the order of G. Seeking a 2-dimensional analogue of Gaydarov and Hopkins' results, I will then characterize the overlap between G-parking functions and 2-dimensional U-parking functions, i.e., pairs of integer sequences whose order statistics are bounded by certain weights along lattice paths in the plane. This talk is based on joint work with Catherine Yan.
Free Probability and Operators
Time: 4:00PM - 5:00PM
Location: BLOC 306
Speaker: Michael Anshelevich, TAMU
Title: Types of noncommutative independence and asymptotics of random matrices.
Abstract: We will discuss how the asymptotic joint distribution of two random matrices "in a general position" can be described using cyclic c-freeness and its particular cases; or, conversely, how different types of noncommutative independence can be asymptotically modeled by random matrices. In the first talk we will concentrate on algebraic independence theories; in the second and third talks, we will explain the connection with random matrices. The talks are based primarily on the articles arXiv:2207.06249 by Cébron and Gilliers; and arXiv:2205.01926 by Cébron, Dahlqvist, and Gabriel.
