Logo

Mathematical Sciences Research Institute

Home » Workshop » Schedules » The saddle connection complex

The saddle connection complex

Holomorphic Differentials in Mathematics and Physics November 18, 2019 - November 22, 2019

November 18, 2019 (04:00 PM PST - 05:00 PM PST)
Speaker(s): Anja Randecker (University of Toronto)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video
No Video Uploaded
Abstract

A half-translation surface is given by a quadratic differential on a closed Riemann surface. It can be visualized by polygons in the plane whose edges are identified via translations and reflection-translations. The geometric properties of a half-translation surface can be captured in the saddle connection complex. The vertices of this complex are saddle connections (i.e. geodesic segments that connect a zero or pole to a zero or pole) and the simplices are formed by saddle connections that are non-intersecting. I will explain properties of the saddle connection complex, in particular the following rigidity result: Every simplicial isomorphism between the saddle connection complexes of two half-translation surfaces is induced by an affine diffeomorphism between the underlying surfaces. The talk is based on joint work with Valentina Disarlo and Robert Tang.

Supplements No Notes/Supplements Uploaded
Video/Audio Files
No Video Files Uploaded