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Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Fall 2019

date speaker title host(s)
Sept 6 Will Sawin (Columbia) On Chowla's Conjecture over F_q[T] Marshall
Sept 13 Yan Soibelman (Kansas State) Riemann-Hilbert correspondence and Fukaya categories Caldararu
Sept 16 Monday Room 911 Alicia Dickenstein (Buenos Aires) TBA Craciun
Sept 20 Jianfeng Lu (Duke) TBA Qin
Sept 27 Omer Mermelstein (Madison) Andrews
Oct 4
Oct 11 Shamgar Gurevich (Madison) Harmonic Analysis on GL(n) over Finite Fields Marshall
Oct 18 Thomas Strohmer (UC Davis) Gurevich
Oct 25
Nov 1 Elchanan Mossel (MIT) Distinguished Lecture Roch
Nov 8 Reserved for job talk
Nov 15 Reserved for job talk
Nov 22 Reserved for job talk
Nov 29 Thanksgiving
Dec 6 Reserved for job talk
Dec 11 Wednesday Nick Higham (Manchester) LAA lecture Brualdi
Dec 13 Reserved for job talk

Spring 2020

date speaker title host(s)
Jan 24 Reserved for job talk
Jan 31 Reserved for job talk
Feb 7 Reserved for job talk
Feb 14 Reserved for job talk
Feb 21
Feb 28 Brett Wick (Washington University, St. Louis) Seeger
March 6 Jessica Fintzen (Michigan) Marshall
March 13
March 20 Spring break
March 27 (Moduli Spaces Conference) Boggess, Sankar
April 3 Caroline Turnage-Butterbaugh (Carleton College) Marshall
April 10 Sarah Koch (Michigan) Bruce (WIMAW)
April 17
April 24 Natasa Sesum (Rutgers University) Angenent
May 1 Robert Lazarsfeld (Stony Brook) Distinguished lecture Erman


Will Sawin (Columbia)

Title: On Chowla's Conjecture over F_q[T]

Abstract: The Mobius function in number theory is a sequences of 1s, -1s, and 0s, which is simple to define and closely related to the prime numbers. Its behavior seems highly random. Chowla's conjecture is one precise formalization of this randomness, and has seen recent work by Matomaki, Radziwill, Tao, and Teravainen making progress on it. In joint work with Mark Shusterman, we modify this conjecture by replacing the natural numbers parameterizing this sequence with polynomials over a finite field. Under mild conditions on the finite field, we are able to prove a strong form of this conjecture. The proof is based on taking a geometric perspective on the problem, and succeeds because we are able to simplify the geometry using a trick based on the strange properties of polynomial derivatives over finite fields.

Yan Soibelman (Kansas State)

Title: Riemann-Hilbert correspondence and Fukaya categories

Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence for differential, q-difference and elliptic difference equations in dimension one. This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles should appear as harmonic objects in this generalized non-abelian Hodge theory. All that is a part of the bigger project ``Holomorphic Floer theory", joint with Maxim Kontsevich.

Shamgar Gurevich (Madison)

Title: Harmonic Analysis on GL(n) over Finite Fields.

Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or 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.

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 certain random walks.

This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)

Past Colloquia


Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012