Séminaire Géométrie et applications
organisé par l'équipe Géométrie
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Thomas Delzant
Anneaux de groupe et géométrie hyperboliques
2 octobre 2023 - 15:30Salle de séminaires IRMA
En faisant opérer un groupe G dans un espace hyperbolique (par exemple un arbre), on peut déduire des propriétés de son anneau C[G] (diviseurs de zéro, éléments inversibles...) -
Peter Albers
Monotone twist maps and Dowker-type theorems
13 novembre 2023 - 15:30Salle de séminaires IRMA
Consider for every natural number n the minimal area of an n-gon circumscribed about a fixed oval in the plane (or maximal area of an inscribed n-gon, or replace area by perimeter). These four sequences satisfy a convexity / concavity property which was first proved by Dowker for area and Molnár resp. Eggleston for perimeter. We show that these four results are all incarnations of the convexity property of Mather's \beta-function of the respective billiard-type systems. We then derive new geometric inequalities of similar type for various other billiard system. Some of these billiards have been thoroughly studied, and some are novel. Moreover, we derive new inequalities (even for conventional billiards) for higher rotation numbers. This is joint work with Sergei Tabachnikov.