Colloquium du laboratoire Dieudonné - lundi 11 février à 14:30

La prochaine séance commune du Colloquium des laboratoire Dieudonné et projet UCA/JEDI MATHIT aura lieu le lundi 11 février à 14:30 en salle de conférences. Elle sera suivie d'une pause-café en salle café. Notre conférencier sera :

Alfonso SORRENTINO (Università degli Studi di Roma Tor Vergata,

et le titre de son exposé sera :

'Dynamical and Spectral Properties of Mathematical Billiards'.

Un résumé est le suivant.

A Mathematical Billiard is a system describing the inertial motion of a point mass inside a domain, with elastic reflections at the boundary. This simple model has been first proposed by G.D. Birkhoff as a mathematical playground where “the formal side, usually so formidable in dynamics, almost completely disappears and only the interesting qualitative questions need to be considered”.

Since then billiards have captured much attention in many different contexts, becoming a very popular subject of investigation. Despite their apparently simple (local) dynamics, their qualitative dynamical properties are extremely non-local. More remarkably, their dynamics is profoundly intertwined with their geometric properties (e.g. the shape of the billiard table): while it is evident how the shape determines the billiard dynamics, a more subtle and difficult question is to which extent the knowledge of the dynamics allows one to reconstruct the shape of the billiard domain. This translates into many intriguing unanswered questions and difficult conjectures that have been the focus of very active research over the last decades.

In this talk I shall focus on several of these questions. In particular, I shall describe some recent results related to the classification of integrable billiards (also known as "Birkhoff conjecture"), and to the possibility of inferring dynamical information on the billiard map from its Length Spectrum (i.e., the collection of lengths of its periodic orbits).

Venez Nombreux !

L'équipe Colloquium