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Monday, April 22, 2019
5:30 PM - 6:30 PM

Caltech/USC/UCLA Joint Topology Seminar

Counting square-tiled surfaces with prescribed real and imaginary foliations
Francisco Arana Herrera, Department of Mathematics, Stanford University,

USC KAP 414

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 Mirzakhani’s work. In this talk we explore the connections between these counting problems, showing they are related by more than just an accidental coincidence.

For more information, please contact Math Dept. by phone at 626-395-3817 or by email at mathinfo@caltech.edu.