Geometric inequalities via information theory

High Dimensional Seminar
Wednesday, September 11, 2019 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Jing Hao – Georgia Tech – jhao6@gatech.edu
Galyna Livshyts

Using ideas from information theory, we establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions.  In the first part of the talk, we derive volume bounds for convex bodies using generalized subadditivity properties of entropy combined with entropy bounds for log-concave random variables. In the second part, we investigate a new notion of Fisher information which we call the L1-Fisher information and show that certain superadditivity properties of the L1-Fisher information lead to lower bounds for the surface areas of polyconvex sets in terms of its slices.