SMS scnews item created by Hannah Bryant at Mon 24 Aug 2020 1456
Type: Seminar
Modified: Mon 24 Aug 2020 1510; Wed 9 Sep 2020 1202
Distribution: World
Expiry: 23 Nov 2020
Calendar1: 8 Oct 2020 1100-1230
CalLoc1: Zoom
CalTitle1: (UPDATE) SMRI Algebra and Geometry Online: Gurevich -- Harmonic Analysis on GLn over Finite
Auth: hannahb@ (hbry8683) in SMS-LDAP

SMRI Algebra and Geometry Online

Harmonic Analysis on GLn over Finite Fields


SAGO Seminar

'Harmonic Analysis on GLn over Finite Fields'

Shamgar Gurevich (University of Wisconsin, Madison)

***NOTE UPDATED TIME*** Thursday 8th October 11:00am -12:30pm (AEST) ***NOTE UPDATED TIME***

Online via Zoom

Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:

Trace(ρ(g)) / dim(ρ),

for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.

Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank.

Rank suggests a new organization of representations based on the very few "Small" ones. This stands in contrast to Harish-Chandra’s "philosophy of cusp forms", which is (since the 60s) the main organization principle, and is based on the (huge collection) of "Large" representations.

This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for random walks.

This is joint work with Roger Howe (Yale and Texas A&M). The numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).

Register here

ball Calendar (ICS file) download, for import into your favourite calendar application
ball UNCLUTTER for printing
ball AUTHENTICATE to mark the scnews item as read
School members may try to .