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Recent progress on the KLS conjecture and Eldan鈥檚 stochastic localization scheme

Department Colloquium

Recent progress on the KLS conjecture and Eldan鈥檚 stochastic localization scheme

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Yuansi Chen, ETH Z眉rich

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笔补蝉蝉肠辞诲别听谤别辩耻颈谤别诲


Kannan, Lov谩sz 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).听听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.

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