Geometry of the moduli space of abelian differentials

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• Ursula Hamenstadt, Bonn
• Wednesday 02 December 2015, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

The moduli space of holomorphic one-forms on Riemann surfaces of fixed genus g admits a natural action of the group SL(2,R) which has a very elementary description. So-called algebraically primitive Teichmueller curves are closed orbits which correspond to Riemann surfaces with special properties.

We outline how classical tools from symplectic and complex geometry together with the groundbreaking work of Eskin, Mirzakhani and Mohammadi (whose main statement is easy to understand) can be used to show that for g at least three, there are only finitely many such orbits. We also discuss some examples.

This talk is part of the Differential Geometry and Topology Seminar series.

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