Campuses:

On Log-Concave Functions

Monday, April 27, 2015 - 10:50am - 11:40am
Keller 3-180
Andrea Colesanti (Università di Firenze)
In this lecture we will review some classic and more recent results on the class of log-concave functions, focusing on the analogies with the theory of convex bodies. We will be particularly interested in functional inequalities. The main example will be the Prékopa-Leindler inequality, that we will present along with its infinitesimal version; but we will also see other examples like the functional versions of the Blashke-Santaló inequality and of Rogers-Shephard inequality. Another topic that we will touch is the possibility to extend to these functions the notions of intrinsic and mixed volumes, as well as the study of valuations.
MSC Code: 
39B62