### Recent progress on the KLS conjecture and Eldan’s stochastic localization scheme

Combinatorics Seminar

19th January 2021, 11:00 am – 12:00 pm

Virtual (online) Zoom seminar; a link will be sent to the Bristol Combinatorics Seminar and Bristol Probability Seminar mailing lists., the week before the seminar.

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, namely Eldan's stochastic localization scheme, which results in the current best bounds of the Cheeger isoperimetric coefficient in the KLS conjecture.

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