##### Department of Mathematics,

University of California San Diego

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### Postdoc seminar

## Anthony Sanchez

#### UCSD

## Translation surfaces and renormalization dynamics

##### Abstract:

A translation surface is a collection of polygons with edge identifications given by translations. In spite of the simplicity of the definition, the space of translation surfaces has connections to different areas of math such as the moduli space of hyperbolic surfaces. A guiding principle centers on turning questions on a *fixed* translation surface into a dynamical one on the space of *all* translation surfaces. We consider an instance of this philosophy related to the slope gap distribution of holonomy vectors of a translation surface. We use this as a jumping off point to consider expanding translates in different spaces such as non-arithmetic hyperbolic manifolds. Aspects of this talk represent different works with L. Kumandari and J. Wang, and with K. Ohm.

### January 25, 2024

### 3:00 PM

APM 5829

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