Linking in torus bundles and Hecke L functions (Nicolas Bergeron, ENS Paris)

04.04.2019 16:15

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.

PS. The Colloquium will be followed by an aperitif

Lieu

Room 17

entrée libre