Séminaire - Septembre
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: septembre.pdf.
- 09/09/2026 - Mingkun Liu (Université Paris 13)
salle Maurice Frechet (ex-salle 05)
Titre: Exact
curve counting on the once-punctured torus
Resumé: 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.