Speaker: Julianna Tymoczko, University of Michigan

Title: Geometric representations of the permutation group

Abstract: In 1976, Springer discovered the remarkable fact that the permutation group acts naturally on (the cohomology of) a collection of algebraic varieties, now called Springer fibers. Indeed, all of the irreducible representations--the building blocks of an arbitrary representation--can be constructed by examining the permutation action on a handful of these Springer fibers. Springer's original construction was completely algebraic but was followed by intense activity on the part of many people to give more intrinsically geometric explanations for these representations. We begin by presenting a sketch of Springer theory using one of these geometric descriptions. Amazingly, we will be able to do this using nothing other than linear algebra. We will then discuss a natural generalization of Springer fibers called Hessenberg varieties, a family of varieties with close ties to many fields, including number theory, numerical analysis, and combinatorics.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491