Sampling a point from a convex body is a problem more general than convex optimization. In this talk, we will give a new algorithm that takes O~(n^3) time (under the KLS conjecture) and O~(n^3.5) time (unconditionally). This is the first general improvement on the Lovász-Vempala O~(n^4) algorithm from 2003.

Joint work with He Jia, Aditi Laddha, and Santosh Vempala.