### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

APRIL 6, 2018

**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

**Time:** Friday, April 6, 2018, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

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