Haonan Zhang (University of South Carolina)
Abstract: Recently, Eldan and Gross developed a stochastic analysis approach to proving functional inequalities on discrete hypercubes. Motivated by a conjecture of Talagrand, one of their main results relates to the sensitivity, variance, and influences of Boolean functions. In this talk, I will discuss an alternative proof of this inequality based on hypercontractivity and an isoperimetric-type inequality of the heat semigroup. Our proof also extends to biased hypercubes and continuous spaces with positive Ricci curvature lower bounds in the sense of Bakry and Émery. This is based on joint work with Paata Ivanisvili.
