学术报告（David Aulicino 2025.1.13）

摘要：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. All necessary

background will be given. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter,

and Martin Schmoll.