—  Mathematics & Statistics

Algebra and Combinatorics Seminar, Fall 2015

Wednesdays 3:40-4:30 1102 BVM hall

Next semester
Previous semesters

Organizers:  Aaron Lauve, Peter Tingley



September
2

9
Peter Tingley
Root multiplicities and Dyck paths
17 *Thursday*
Ben Webster (Virginia)
Gradings on (q-)Schur algebras and quiver representations
23
Aaron Lauve (Loyola)
October
1 *Thursday*
Jean-Baptiste Priez (Paris-Sud)
7

14
Jonathan Kujawa (U. of Oklahoma)
21

28

November
4
11
Robert Muth (University of Oregon)
18

25
No talk (thanksgiving)
December
2



Directions

IES (the institute for environmental sustainability) is located at the corner of W. Sheridan and N. Kenmore Avenues, Chicago, IL (map)

Parking is available on-campus for $7 in the Parking Garage (building P1 on the Lake shore campus map). To get to the Parking Garage, enter campus at the corner of West Sheridan Road and North Kenmore Avenue.

Abstracts

Sept 9: Peter Tingley (Loyola), Root multiplicities and Dyck paths

I will discuss a way to calculate root multiplicities for indefinite Kac-Moody algebras by counting rational Dyck paths subject to various conditions. The conditions are very complicated, so exact calculation is non-trivial, but the method gives good asymptotics, at least in small rank. Well, that last is partially conjecture, but it is based on solid heuristics and computer evidence, provided by Colin Williams. The mathematical justification for all this goes through quiver varieties, and I'll explain some of that as well.

Sept 17: Ben Webster (Virginia), Gradings on (q-)Schur algebras and quiver representations

I'll explain a method for obtaining a surprising grading on (q-)Schur algebras. This grading is quite boring in the case where this algebra is semi-simple, but over a finite field, or when q is a root of unity, it's very interesting. As time allows, I'll discuss how this presentation is inspired by the geometry of quiver varieties, and how it relates to Kazhdan-Lusztig polynomials, Fock space and the representation theory of affine Lie algebras.