Systols on Origami Translation Surfaces

15.06.2021 15:00 - 17:00

Gabriela Weitze-Schmithüsen (Universität des Saarlandes)

Finite translation surfaces are obtained by a charming concrete construction: take finitely many polygons in the Euclidean plane and glue pairs of their edges via translations such that you obtain a connected surface. This naturally defines a Riemann surface X of some genus g together with a holomorphic differential. The moduli space of translation surfaces of genus g is stratified by orders of the zeroes of these differentials.

Although translation surfaces have been intensively studied since the 1980’s, there are natural questions which are still wildly open. One of these questions is: What is the maximal systolic ratio in a given stratum, i.e. the maximal length of a shortest curve among all surfaces of area 1. We study this question in the stratum H_2(1,1) of genus 2 surfaces with two zeroes of order 1. This is joint work with Columbus, Herrlich and Mützel.



G. Arzhantseva, A. Evetts
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