Speaker: Aiya Kuchukova (Georgia Institute of Technology)
Title: Sampling equitable colorings and beyond
Abstract: We explore a problem at the intersection of graph theory, sampling and statistical physics: is it possible to approximately sample a uniform equitable coloring? (Equitable colorings are such that each pair of color class sizes differs by at most 1.) To answer this question, we generalize a lot of existing tools such as zero-freeness of Potts model, Central Limit Theorem, and Local Central Limit Theorem from univariate to multivariate. The talk will not require any knowledge of sampling or statistical physics. Joint work with Will Perkins and Xavier Povill.