Recent Progress on the KLS Conjecture

Explore recent advancements in the Kannan-Lovász-Simonovits (KLS) conjecture in this 42-minute lecture by Yuansi Chen at the Hausdorff Center for Mathematics. Delve into the origins and significant implications of the KLS conjecture, including its connections to Bourgain's slicing conjecture and the thin-shell conjecture. Examine the evolution and refinement of the primary proof technique, Eldan's stochastic localization scheme, and its role in establishing the current best bounds for the Cheeger isoperimetric coefficient. Gain insights into key concepts such as log-concave density, half-spaces, and universal constants as they relate to this important mathematical problem.

Introduction
KLS conjecture
Universal constants
CMC sampling
Proof of KLS conjecture
Stochastic localization
Line control