Seminariet i Algebraisk geometri och talteori

​Alex Kontorovich, Rutgers University: Asymptotic Length Saturation for Zariski Dense Surfaces


Abstract: The lengths of closed geodesics on a hyperbolic manifold are determined by the traces of its fundamental group. When the latter is a Zariski dense subgroup of an arithmetic group, the trace set is contained in the ring of integers of a number field, and may have some local obstructions. We say that the surface's length set "saturates" (resp. "asymptotically saturates") if every (resp. almost every) sufficiently large admissible trace appears. In joint work with Xin Zhang, we prove the first instance of asymptotic length saturation for punctured covers of the modular surface, in the full range of critical exponent exceeding one-half (below which saturation is impossible).

The seminar is given in Zoom: https://chalmers.zoom.us/j/68521024554

​Organisers: Anders Södergren (andesod@chalmers.se) and Christian Johansson (chrjohv@chalmers.se). Please contact one of us if you wish to be informed of future seminars.
Kategori Seminarium
Plats: Online
Tid: 2021-12-08 16:15
Sluttid: 2021-12-08 17:15

Sidansvarig Publicerad: fr 03 dec 2021.