Convex-body Sampling to the Kannan-Lovász-Simonovits Conjecture

Sampling uniformly from a convex body links randomized volume computation to the Kannan–Lovász–Simonovits conjecture. This talk identifies geometric quantities controlling sampler mixing and introduces stochastic localization as a way to bound them, including a simple argument yielding a polylogarithmic, though nonoptimal, bound.