Geometry Seminar

---

Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces

Speaker: David Aulicino, Brooklyn College/CUNY

Location: Warren Weaver Hall 1314 in person and on Zoom

Date: Tuesday, April 22, 2025, 6 p.m.

Synopsis:

We consider generic translation surfaces of genus \(g>0\) with 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. For these cyclic covers, several surprising aspects emerge among their Siegel-Veech constants.

All necessary background will be given, and computational aspects of the computer experiments that inspired the work will be highlighted.

This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.

Notes:

In person.  Also simultaneously broadcast on Zoom, contact Boris Aronov for meeting ID.