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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.