Séminaire Analyse Harmonique
Orthospectrum of convex bodies and Poisson formulas
Jan. 2023
Intervenant : Gabriel Rivière
Institution : Université de Nantes
Heure : 14h00 - 15h00
Lieu : salle 2L8
I will start by decribing two "variants" of the Poisson formula that are due to Guinand and Meyer. I will then show how these two formulas can be interpreted in terms of the orthospectrum (a family of characteristic lengths) of two convex bodies. With that interpretation in mind, Guinand-Meyer's formulas correspond to the case where the convex bodies are reduced to two points 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.
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