Systoles sur les origamis

Gabriela Weitze-Schmithüsen
Universität des Saarlandes, Saarbrücken (Germany)
https://www.math.uni-sb.de/ag/weitze/CMS/index.php/en/people/weitze-schmithuesen

Date(s) : 09/04/2021 iCal
11h00 - 12h00

Although translation surfaces have been intensively studied since the 1980’s, there are still many natural questions wildly open.

One of these questions is: what is the maximal systolic ratio in a stratum, i.e. what is the maximal length of a shortest simple closed geodesic on a translation surface of area 1 in a fixed stratum? We study this question of translation surfaces of genus 2 with two singularities.

This is joint work with Colombus, Herrlich, Mützel.

https://arxiv.org/abs/1809.10327

An origami O with 30 squares whose systole is √17. O has two singularities • and ◦.
The dashed line is a systole (arxiv.org/abs/1910.0845, fig.4, page 23)