Divergence and Entropy inequalities for log concave functions
Dr. Umut Caglar, FIU
October 29, 3.30 pm, rm. DM 190
Title: Divergence and Entropy inequalities for log concave functions
Abstract: It has been a major focus of research in convex geometry in recent years, to extend notions and inequalities from the class of convex bodies to classes of functions.
In this talk we obtain analytic versions of several geometric invariants and inequalities. In particular, we prove new entropy inequalities for log concave functions that strengthen and generalize recently established reverse log Sobolev inequality for such functions. This leads naturally to the concept of f-divergence and, in particular, relative entropy for log concave functions. We establish their basic properties, among them the affine invariant valuation property. We also give applications in the theory of convex bodies.