Mon, 10 Feb 2025
14:15
L5

The Schubert variety of a hyperplane arrangement

Nick Proudfoot
(University of Oregon)
Abstract

I’ll tell you about some of my favorite algebraic varieties, which are beautiful in their own right, and also have some dramatic applications to algebraic combinatorics.  These include the top-heavy conjecture (one of the results for which June Huh was awarded the Fields Medal), as well as non-negativity of Kazhdan—Lusztig polynomials of matroids.

Fri, 29 Nov 2024
12:00
L2

Towards a mathematical definition of superstring scattering amplitudes

Alexander Polishchuk
(University of Oregon)
Abstract

This is a report on the ongoing joint project with Giovanni Felder and David Kazhdan. I'll describe a conjectural way to set up the integration of the superstring measure on the moduli space of supercurves, including a brief review of the necessary supergeometry. The main theorem is that this setup works for genus 2 with no punctures.

Mon, 18 Nov 2024
15:30
L5

Equivariant log concavity and representation stability

Nicholas Proudfoot
(University of Oregon)
Abstract

June Huh proved in 2012 that the Betti numbers of the complement of a complex hyperplane arrangement form a log concave sequence.  But what if the arrangement has symmetries, and we regard the cohomology as a representation of the symmetry group?  The motivating example is the braid arrangement, where the complement is the configuration space of n points in the plane, and the symmetric group acts by permuting the points.  I will present an equivariant log concavity conjecture, and show that one can use representation stability to prove infinitely many cases of this conjecture for configuration spaces.
 

Mon, 20 Mar 2023
14:15
L3

The asymptotic geometry of the Hitchin moduli space

Laura Fredrickson
(University of Oregon)
Abstract

Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichmüller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperkähler metric.  An intricate conjectural description of its asymptotic structure appears in the work of Gaiotto-Moore-Neitzke and there has been a lot of progress on this recently.  I will discuss some recent results using tools coming out of geometric analysis which are well-suited for verifying these extremely delicate conjectures. This strategy often stretches the limits of what can currently be done via geometric analysis, and simultaneously leads to new insights into these conjectures.

Tue, 09 Jun 2020
14:15
L4

TBA

Alexander Kleshchev
(University of Oregon)
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