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Counting square-tiled surfaces with prescribed real and imaginary foliations

Banff International Research Station for Mathematical Innovation and Discovery

Let X be a closed, connected, hyperbolic surface of genus 2. Is it more likely for a simple closed geodesic on X to be separating or non-separating How much more likely In her thesis, Mirzakhani gave very precise answers to these questions. One can ask analogous questions for square-tiled surfaces of genus 2 with one horizontal cylinder. Is it more likely for such a square-tiled surface to have separating or non-separating horizontal core curve How much more likely Recently, Delecroix, Goujard, Zograf, and Zorich gave very precise answers to these questions. Surprisingly enough, their answers were exactly the same as the ones in Mirzakhaniâs work. In this talk we explore the connections between these counting problems, showing they are related by more than just an accidental coincidence.

Mathematics; Dynamical systems and ergodic theory; Algebraic geometry; Dynamical systems

video/mp4

Author affiliation: Stanford University

2019-11-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72423

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/