SL(2,Z)-orbits of genus two square-tiled surfaces

Luke Jeffreys

Friday 14th February, 2020 14:00-15:00 Maths 311B


A square-tiled surface is an important example of an Abelian differential on a Riemann surface. The moduli space of Abelian differentials is a central object of study in Teichmüller theory, and square-tiled surfaces have played a key role in this area of modern research. In this talk, I will introduce square-tiled surfaces and discuss the classification of their SL(2,Z)-orbits in the particular case of genus two (with one zero for the Abelian differential). This work was carried out by Hubert-Lelièvre and McMullen.

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