Combinatorics, computing, and k-Schur functions
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.