Colloque des sciences mathématiques du Québec

8 octobre 2021 de 11 h 00 à 12 h 00 (heure de Montréal/HNE)

(Conférence Nirenberg) Progrès récents sur la conjecture de Kannan-Lovasz-Simonovits (KLS) et le problème des sections de Bourgain II

Colloque par Yuansi Chen (Duke University)

In recent work, Chen (2020) improved Eldan's stochastic localization proof technique, which was deployed in Lee and Vempala (2017), to prove an almost constant Cheeger isoperimetric coefficient in the KLS conjecture with dimension dependency d^o(1).  Consequently, his proof also provides a substantial advance toward the resolution of Bourgain's slicing conjecture and the thin-shell conjecture.  After getting conformable with Eldan's stochastic localization technique, in this talk we navigate through how to refine the technique to provide the current best bound.  We will complete the self-contained proof of Chen (2020) and highlight the new ideas involved.  Finally, we will discuss some extensions and provide an outlook for future research directions.


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