Local maxima of the systole function

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.