The Eldan-Gross Inequality - From Boolean Functions to Continuous Spaces

Explore a 53-minute mathematics lecture that delves into an alternative proof of the Eldan-Gross inequality, which connects sensitivity, variance, and influences of Boolean functions on discrete hypercubes. Learn about the stochastic analysis approach developed by Eldan and Gross, motivated by Talagrand's conjecture, and discover how hypercontractivity and isoperimetric-type inequality of the heat semigroup can be used to prove these relationships. Examine how this proof extends beyond the original scope to include applications in biased hypercubes and continuous spaces with positive Ricci curvature lower bounds, as defined by Bakry and Émery. Based on collaborative research with Paata Ivanisvili, gain insights into this significant mathematical advancement presented at the Hausdorff Center for Mathematics.