Speaker: Jennifer Morse, University of Virginia

Title: Combinatorics, computing, and k-Schur functions

Abstract: Combinatorial structures have been used to give efficient and elegant constructions for polynomial coefficients going back to the binomial theorem. In turn, a wide spectrum of problems can be converted to computations with appropriate polynomials. We will first see how this plays out on century-old examples from representation theory and geometry and then discuss a more contemporary example.

In particular, computing with a distinguished family of symmetric polynomials called k-Schur functions has recently been tied to the problem of computing string theory invariants named for Gromov and Witten and to characterizing the irreducible decomposition of certain bi-graded (Garsia-Haiman) modules. However, the intricacy of the k-Schur definition has been a major obstruction to pinning down rules for computation. We will discuss new developments in this direction.

A background in elementary linear algebra should do.

The work is joint with J. Blasiak, A. Pun, and D. Summers

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