An online seminar, usually held every couple of weeks, featuring invited speakers from around the world. Open to all; connection details are shared ahead of each talk.
To be added to the mailing list and receive announcements about future talks, sign up here.
We survey progress from the past five years on the distribution of mass in high-dimensional convex bodies and in probability distributions with convexity properties. The concentration of measure phenomenon has traditionally been studied in highly regular or structured settings, such as spheres, Hamming cubes, Gaussian measures, Markov chains, and martingales. It turns out that convexity assumptions provide an alternative source of regularity in high dimensions with remarkably similar features: Lipschitz functions are highly concentrated, half-spaces are nearly optimal in the isoperimetric problem, and the central limit theorem is nearly as strong as in the setting of independent random variables. We will also discuss the role of Bourgain’s slicing problem as a driving force behind advances in our understanding of the convexity assumption in high dimensions. Based on joint works with P. Bizeul and J. Lehec.
Abstract to be announced.
Abstract to be announced.
Abstract to be announced.