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Department of Mathematics, Applied Mathematics and Statistics

Tuesday, March 4, 2014 (4:15 p.m., Yost 306)

Title: Divergence and Entropy Inequalities
for Log Concave Functions

Speaker: Umut Caglar (Case Western Reserve University)
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. This is also a main topic of this dissertation. 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 and Poincare inequalities 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.