³ÉÈË´óƬ

Curves Seminar

Speaker: Trevor Shillington

Affiliation: ³ÉÈË´óƬ

Title: Symmetric Polynomials and Functions

Abstract: In this talk, we will attempt to wrap up the combinatorics and pave the way to representation theory by investigating symmetric polynomials. This will include the interconnectedness of different types of symmetric polynomials, as well as prove one of the Jacobi-Trudi identities that has been teased before: Jacobi’s original definition of the Schur polynomials. We will wrap-up with defining the ring of symmetric functions and investigating some of the geometry they can be given and how this ring unifies identities about symmetric polynomials.