Systoles in translation surfaces

translation surfaces
Teichmüller dynamics mapping class groups and applications
eem2018
Grenoble
[MATH]Mathematics [math]
Systoles

Apparaît dans la collection : Summer School 2018 - Teichmüller dynamics, mapping class groups and applications.

I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1). We also determine the maximum systolic ratio (length squared/area) in H(2g-2), and we give a conjectural value for maximum systolic ratio in H(1,1).