Per Alexandersson: Two open problems on symmetric functions obtained from colorings - an unexpected relationship

Abstract: We relate the Stanley-Stembridge conjecture with a certain positivity conjecture on certain LLT polynomials. Both are major open problems in algebraic combinatorics. We look at some of the combinatorial objects that arise in the study of these functions, and different possible approaches. Bonus problem depending on time/interest: A combinatorial interpretation of certain volumes of moduli spaces?