The stochastic localization technique was first used by Eldan in 2012 to show that the optimal constants (with respect to the dimension) in the thin shell conjecture, and the conjecture by Kannan, Lovasz, and Simonovits (KLS) are equivalent up to logarithmic factors. Since then, it has also found other applications in convex geometry and probability. In particular, Lee and Vempala used it to improve the best known constant in the KLS conjecture.

In this talk, I will provide brief background on the KLS conjecture and some related conjectures. Then I will describe the stochastic localization scheme of Eldan and explain its main properties. Speaker(s): Alon Nishry (University of Michigan)