Quebec Mathematical Sciences Colloquium

April 12, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Linking in torus bundles and Hecke L functions

Colloquium presented by 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.


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