Szego Seminar: "Representation Theory and Algebraic Combinatorics"

Speaker: Nathan Lesnevich, Washington University in Saint Louis

Abstract: Representation theory seeks to study algebraic structures by representing them as linear transformations over a (complex) vector space, which allows for the application of well-known tools in linear algebra. In this talk, we will give an introduction to representations of the symmetric group, and of symmetric functions. Our goal is to show how one might study more "traditional" problems in representation theory with combinatorics via symmetric functions. In particular, we will define the inner products of both the character space and the algebra of symmetric functions and give their isometry via the Frobenius characteristic map. We'll end by giving some open problems in chromatic symmetric functions and discussing their implications in representation theory.

 

Host: Nathan Wagner