Square-tiled surfaces

Elise Goujard (Paris-Sud)

Monday 23rd January, 2017 16:00-17:00 Maths 204


Dynamics in rational polygonal billiards is strongly related to dynamics and geometry in the moduli spaces of flat surfaces. In particular, evaluating the Masur-Veech volumes of such moduli spaces and computing Siegel-Veech constants give some quantitative results for the dynamics in the associated billiards. This evaluation can be done by counting square-tiled surfaces, with and without weight.

I present several results about square-tiled surfaces related to this problem (joint work with M.Möller and with V. Delecroix, P. Zograf, A. Zorich) and explain their relation with the Eskin-Zorich conjectures on the large genus asymptotics of the Masur-Veech volumes. 

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