Proving that various families of symmetric functions have positive coefficients with respect to the Schur function basis is a central problem in algebraic combinatorics. Jonah Blasiak and Sergey Fomin have recently developed a very general framework for combinatorially proving Schur positivity, which encompasses many previously used techniques.

In this talk, I'll explain their framework, and use it to give a quick proof that Stanley symmetric functions are Schur positive. Then I'll say something about switchboards and the new results (and conjectures) arising from their work. Speaker(s): Gabriel Frieden (University of Michigan)