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

## Description of video

 Date: 10/21/22 Speaker : Ivanov Grigory

## Keywords

We will discuss a simple way of representing $1/s$-concave functions on ${\mathbb{R}}^{d}$ as convex bodies in ${\mathbb{R}}^{d+1},$ 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.

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