Local maxima of the systole function

Maxime Fortier-Bourque (Glasgow)

Monday 1st October, 2018 16:00-17:00 Maths 311B


The systole of a hyperbolic surface is the length of any of its shortest closed geodesics. Schmutz Schaller initiated the study of the systole function and its local maxima in the 90's. I will explain a construction of a new infinite family of closed hyperbolic surfaces which are local maxima for the systole. The simplest of these surfaces is the Bolza surface, which is the surface of genus 2 with the largest number of symmetries. In higher genus, we obtain super-exponentially many examples and most of them have a trivial automorphism group. This is joint work with Kasra Rafi.

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