Séminaires : Séminaire Géométrie et dynamique dans les espaces de modules

Séminaire mensuel à l'Institut Henri Poincaré, plupart du temps mercredi de 14h à 15h salle Olga Ladyjenskaïa (ex-salle 01). Pour plus de détails voire la page web :

http://carlos.matheus.perso.math.cnrs.fr/seminaire/index.html

Monthly seminar at the Institute Henri Poincaré. It usually takes place on Wednesday from 2pm to 3pm at the room Olga Ladyjenskaïa (ex-room 01). For more details see

http://carlos.matheus.perso.math.cnrs.fr/seminaire/index.html

Two closed curves on a surface are said to have the same topological type if they lie in the same mapping class group orbit. Mirzakhani first showed that, on a hyperbolic surface, the number of closed geodesics of a given topological type of length at most L is asymptotically proportional to L^{6g-6}. In this talk, we will focus on the case of the once-punctured torus. Rather than using hyperbolic length, we will count curves according to their word length. In this setting, it turns out that exact counting formulas can be obtained. This is joint work with Filippo Baroni and David Fisac.