Seminar: Mark Meckes

Title

Typical Marginals of Convex Bodies

Speaker

Mark Meckes, Case Western Reserve University

Abstract

A recent theorem of Klartag asserts that if X is uniformly distributed in a high-dimensional isotropic convex body, then most linear functionals of X are approximately Gaussian in distribution. This phenomenon has connections with observations going back to Maxwell and Archimedes, with modern roots in the work of Sudakov, Diaconis, and Freedman, among others. I will give a survey of the history of Klartag's theorem, partial results which preceded it and recent developments.