Presenting a proof of the Kannan-Lovasz-Simonovits conjecture

Abstract

Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lov\'asz-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high dimensional geometry in recent decades. We present here a proof of this conjecture. The crucial step in the proof is the very recent criterion from Song and Zhang involving high-order derivatives of tilt averages.