Combinatorics Seminar: Gabriel Necoechea, KSU will talk about "Introduction to Dual Equivalence Graphs"
Gabriel Necoechea, Kansas State University
Title: Introduction to Dual Equivalence Graphs
Abstract: The Schur functions are an important linear basis for symmetric functions. Given some other symmetric functions, one can ask if these symmetric functions are non-negative combinations of Schur functions (i.e. they are Schur-positive), in which case one would like to interpret these coefficients as counting something. The "something" being counted can be representation-theoretic or algebro-geometric or more purely combinatorial. Dual equivalence graphs are a more purely combinatorial "paradigm" for proving that certain families of symmetric functions are Schur-positive. In this talk, we will present the basic data of dual equivalence graphs and illustrate their application in proving Schur-positivity. This talk follows closely "DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY" by Sami Assaf.
Wednesday, October 23 at 3:30pm to 4:20am