Abstract: Kannan, Lovász and Simonovits (KLS) conjectured in 1995 that the Cheeger isoperimetric coefficient of any log-concave density is achieved by half-spaces up to a universal constant factor. This conjecture also implies other important conjectures such as Bourgain's slicing conjecture (1986) and the thin-shell conjecture (2003).  In this talk, first we briefly survey the origin and the main consequences of these conjectures. Then we present the development and the refinement of the main proof technique, Eldan's stochastic localization scheme. Finally we explain a few proof details which result in the current best bound of the Cheeger isoperimetric coefficient in the KLS conjecture.

Zoom Info: 

ID: 654 4393 7829

Password: 657934

Join Zoom Meeting by clicking the link https://zoom.com.cn/j/65443937829?pwd=aXVDZW9uRzF5SmpDaFVNcXRTNmdDZz09