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
Show 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.
