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

Yunbum Kook (Georgia Tech) https://simons.berkeley.edu/talks/yunbum-kook-georgia-tech-2026-09-23 Local to Global Principles Uniform sampling from a convex body is a classical problem in theoretical computer science, closely connected to randomized volume computation in the seminal work of Dyer, Frieze, and Kannan. In this talk, I will use this problem to motivate the geometric quantities that govern the mixing of uniform samplers and explain their connection to the Kannan–Lovász–Simonovits conjecture. I will then review stochastic localization as a tool for handling these quantities and walk through a simple argument that yields a sub-optimal (but still poly-logarithmic) bound.