Per Alexandersson: Symmetric Functions and Graph Colorings

Abstract

 I will give an introduction to the area of symmetric functions. One big open problem in this area is the Stanley-Stembridge conjecture, which involves certain symmetric functions arising from graph colorings. Briefly, the conjecture states that one should be able count colorings of certain graphs with a formula of a particular format. I will give an overview of this problem, and discuss some of my research efforts in this area.