Around Duke's Theorem on equidistribution of closed geodesics

par Asbjørn Nordentoft (Paris 13)

jeudi 2 mars 2023, 14:00 → 15:00 Europe/Paris

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 talk about a number of recent 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 and extended by Humphries-N.). I will emphasize the similarities and differences with the imaginary case. If time permits I will also discuss a $q$-orbit analogue.

 

This is partly based on joint with Peter Humphries, and Ser Tan Peow (in progress).