Hunter Dinkins – GMA Seminar

Title: Symmetric Functions

Abstract: The most basic type of symmetric functions appears when studying roots of a polynomial: the coefficients of a polynomial are the elementary symmetric functions of its roots. Much of mathematics was motivated by trying to write down formulas for the reverse relationship. There are many other types of symmetric functions, which have deep combinatorial and representation theoretic properties. In this talk, I will provide a tour of some of the basic types of symmetric functions and, time permitting, will discuss a neat application of how Schur functions allow us to count 3D partitions.