Title: Needle decomposition and Ricci curvature
Abstract: Needle decomposition is a technique in convex geometry,
which enables one to prove isoperimetric and spectral gap
inequalities, by reducing an n-dimensional problem to a 1-dimensional
one. This technique was promoted by Payne-Weinberger, Gromov-Milman
and Kannan-Lovasz-Simonovits. In this lecture we will explain what
needles are, what they are good for, and why the technique works under
lower bounds on the Ricci curvature.