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Explore a 47-minute lecture by Bo'az Klartag on Yuansi Chen's work regarding the Kannan-Lovasz-Simonovits (KLS) conjecture. Delve into the isoperimetric problem in high-dimensional convex bodies, examining the optimal way to partition a convex body into two equal-volume pieces while minimizing their interface. Learn about the conjecture's suggestion that the optimal solution involves bisecting the convex body with a hyperplane, up to a universal constant. Discover the connection between the KLS conjecture and Bourgain's slicing conjecture, and explore recent significant progress towards both. Study Eldan's Stochastic Localization technique, a key method in addressing these problems. While the lecture aims to minimize prerequisites, some familiarity with log-concave measures and basic concepts in stochastic differential equations may be beneficial. Topics covered include introduction, antitransport, quality, color of B, stochastic differential, change theorem, evolution equation of 80, and proof.
