Around Duke’s theorem on the equidistribution of closed geodesics.

Date/heure
30 janvier 2025
14:30 - 15:30

Lieu
Salle Döblin

Oratrice ou orateur
Asbjørn Christian Nordentoft (Orsay)

Catégorie d'évènement
Séminaire de Théorie des Nombres de Nancy-Metz


Résumé

A celebrated result of Duke from the 80’s says that closed geodesics on the modular curve equidistribute as the discriminant tends to infinfity. This is the real quadratic analogue of the equidistribution of CM-points on the modular curve associated to class groups of imaginary quadratic fields. In this talk I will describe a number of generalizations of the result of Duke including; the distribution of the homology classes of closed geodesics, and hyperbolic orbifolds associated class groups of real quadr. fields (as defined by Duke-Imamouglu-Toth). I will emphasize the similarities and differences with the imaginary case. If time permits I will also discuss a q-orbit analogue.