##### Department of Mathematics,

University of California San Diego

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### Math 211 B00 - Group Actions Seminar

## Aaron Calderon

#### Yale University

## Random hyperbolic surfaces via random flat surfaces

##### Abstract:

What does it mean to pick a ``random'' hyperbolic surface, and how does one even go about ``picking'' one? Mirzakhani gave an inductive answer to this question by gluing together smaller random surfaces along long curves; this is equivalent to studying the equidistribution of certain sets inside the moduli space of hyperbolic surfaces. Starting from first concepts, in this talk Iâ€™ll explain a new method for building random hyperbolic surfaces by building random \emph{flat} ones. As time permits, we will also discuss the application of this technique to Mirzakhaniâ€™s ``twist torus conjecture.'' This is joint work (in progress) with James Farre.

Host: Brandon Seward

### November 4, 2021

### 12:00 PM

### Zoom ID 967 4109 3409 (email an organizer for the password)

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