Salle 2
le 23 février 2024 à 10:45
We consider generic translation surfaces of genus
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
. Given a translation surface, the number of cylinders with waist curve of length at most
grows like
. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by
, the limit as
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
. 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.