Grigory Ivanov: Geometric representation of 1 / s -concave functions and duality

Description of video

Date: 10/21/22
Speaker :Ivanov Grigory

We will discuss a simple way of representing 1/s-concave functions on Rd as convex bodies in Rd+1, which allows us to use both standard ideas of convexity and tricks from the study of log-concave functions. We will discuss the properties of polar'' functions as an application. In particular, we prove that the reciprocal of the integral of the polar function of a log-concave function is log-concave as a function of the center of polarity.