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

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If you have a question about this talk, please contact Dr Sergio Bacallado.

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 almost-constant bound of the Cheeger isoperimetric coefficient in the KLS conjecture.

This talk is part of the Statistics series.

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