Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces

David Aulicino (Brooklyn College)

Monday 31st March 16:00-17:00 Maths 311B

Abstract

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

Add to your calendar

Download event information as iCalendar file (only this event)