Colloque des sciences mathématiques du Québec

12 avril 2019 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Linking in torus bundles and Hecke L functions

Colloque par Nicolas Bergeron (École normale supérieure (Paris), France)

Torus bundles over the circle are among the simplest and cutest examples of 3- dimensional manifolds. After presenting some of these examples, using in particular animations realized by Jos Leys, I will consider periodic orbits in these fiber bundles over the circle. We will see that their linking numbers --- that are rational numbers by definition --- can be computed as certain special values of Hecke L-functions. Properly generalized this viewpoint makes it possible to give new topological proof of now classical rationality or integrality theorems of Klingen-Siegel and Deligne-Ribet. It also leads to interesting new "arithmetic lifts" that I will briefly explain. All this is extracted from an on going joint work with Pierre Charollois, Luis Garcia and Akshay Venkatesh.

Adresse

McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104