##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Prof. Jane Wang

#### University of Maine

## The topology of the moduli space of dilation surfaces

##### Abstract:

Translation surfaces are geometric objects that can be defined as a collection of polygons with sides identified in parallel opposite pairs by translation. If we generalize slightly and allow for polygons with sides identified by both translation and dilation, we get a new family of objects called dilation surfaces. While translation surfaces are well-studied, much less is known about dynamics on dilation surfaces and their moduli spaces. In this talk, we will survey recent progress in understanding the topology of moduli spaces of dilation surfaces. We will do this by understanding the action of the mapping class group on the moduli space of dilation surfaces. This talk represents joint work with Paul Apisa and Matt Bainbridge.

Host: Brandon Seward

### January 25, 2024

### 10:00 AM

Zoom ID 967 4109 3409

Research Areas

Ergodic Theory and Dynamical Systems****************************