Explore the Kannan-Lovasz-Simonovits (KLS) conjecture and recent progress towards its resolution in this 46-minute lecture by Bo'az Klartag. Delve into the isoperimetric problem in high-dimensional convex bodies, examining optimal partitioning methods and their implications. Learn about the connection between the KLS conjecture and Bourgain's slicing conjecture, and discover the key technique of Eldan's Stochastic Localization. Cover topics such as log-concave measures, boundary measure, convexity, partitioning, and normalization. Gain insights into the relevance, applications, and motivations behind this mathematical problem, with a focus on recent proofs and advancements in the field.