# Talk by Gabriel Rivière

On January 10th, 2024, **Gabriel Rivière** (Universität Nantes) gave a talk about **"Orthospectrum of convex bodies and Poisson formulas"** as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.

## Abstract

I will start by describing two ”variants“ of the Poisson formula that are due toGuinand and Meyer. I will then show how these two formulas can be interpreted in terms of the orthospectrum (a family of characteristic lengths) of a convex body. With that interpretation in mind, Guinand-Meyer’s formulas correspond to the case where the convex body is reduced to a point in dimension 3. I will explain how this formula can be extended to two general (strictly) convex bodies and how it encodes certain geometric quantities (mixed volumes). This was obtained in a joint work with Nguyen Viet Dang and Matthieu Léautaud.