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* This talk is intended for faculty, researchers, and students interested in combinatorics and related fields such as physics, computer science, engineering, etc.

Title: New identities in the character table of symmetric groups

Abstract: Amdeberhan proposed equalities of $\Sigma_n$ characters sums over a new set called $Ev(\lambda)$. When investigating the alternating sum of characters for $Ev(\lambda)$ written in terms of the inner product of Schur functions and power sum symmetric functions, we found an equality between the alternating sum of power sum symmetric polynomials and a product of monomial symmetric polynomials. We have also discovered new equalities between sums of degrees of irreducible characters for the symmetric group and a new combinatorial interpretation for the Riordan numbers in terms of degrees of irreducible characters labeled by partitions with three parts of the same parity. This is the first, to our knowledge, theorem about degrees of symmetric group characters with parity conditions imposed on the partitions indexing the characters.This is joint work with David Hemmer and Armin Straub.

Bio: Dr. Karlee Westrem is an Assistant Professor in the Department of Mathematical Sciences at Appalachian State University. She received a PhD in Mathematical Sciences from Michigan Technological University (Advisor: Dr. David Hemmer), a MS in Mathematics from the University of Minnesota Duluth and a BS in Mathematics from the University of North Dakota. Dr. Westrem's research focuses on combinatorial representation theory.