Explore the third part of the second lecture on isoperimetric inequalities in high dimensional convex sets, delivered by Joseph Lehec at the Institut Henri Poincaré. Delve into advanced mathematical concepts related to Bourgain's slicing problem and the Kannan-Lovasz-Simonovits (KLS) isoperimetric conjecture. Gain insights into the complex world of high-dimensional geometry and its applications in convex analysis. This 73-minute lecture is part of a comprehensive IHP school series, featuring lectures by Bo'az Klartag and Joseph Lehec, aimed at deepening understanding of these challenging mathematical problems.