An alternative proof of the slicing conjecture is given through optimal small-ball estimates for isotropic log-concave vectors, using stochastic localization and Guan's bound.
Isoperimetric inequalities in high-dimensional convex sets
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abstract
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).
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The slicing conjecture via small ball estimates
An alternative proof of the slicing conjecture is given through optimal small-ball estimates for isotropic log-concave vectors, using stochastic localization and Guan's bound.