Quebec Mathematical Sciences Colloquium

October 8, 2021 from 11:00 to 12:00 (Montreal/EST time)

(Nirenberg Lecture) Recent progress on the Kannan-Lovasz-Simonovits (KLS) conjecture and Bourgain's slicing problem II

Colloquium presented by 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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