##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## David Aulicino

#### Brooklyn College and the CUNY Graduate Center

## Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces

##### Abstract:

We consider generic translation surfaces of genus g>0 with n>1 marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given and a connection to combinatorics will be presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.

### January 12, 2023

### 10:00 AM

Zoom ID 96741093409

Password 'dynamics'

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