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arXiv:2610.05474math.FA

Presenting a proof of the Kannan-Lovasz-Simonovits conjecture

Pierre Bizeul, Boaz Klartag, Joseph Lehec

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Abstract

Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lovász-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high dimensional geometry in recent decades. We present here a proof of this conjecture. The crucial step in the proof is the very recent criterion from Song and Zhang involving high-order derivatives of tilt averages.

arXiv comments
32 pages, contains a paragraph describing AI use
Journal reference
DOI
Subjects
math.FAFunctional Analysis math.MGMetric Geometry math.PRProbability

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