David Aulicino (Brooklyn College) de 14h a 15h
Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces
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 L2 . By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L2 , 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.
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Anja Randecker (Saarland University, Heidelberg University) de 15h30 a 16h30
Free groups as Veech groups of finite-area translation surfaces
The question of realization of Veech groups is one of the few instances where we know essentially everything about infinite translation surfaces and not so much about finite translation surfaces. An intermediate case between the two extremes is the one of finite-area infinite-genus translation surfaces: while we do not have a classification of groups that can be realized as Veech groups, a careful study of covers of the Chamanara surface shows that every free group appears as projective Veech group.
In this talk, I will introduce the Chamanara surface and its Veech group, explain how to describe all its finite covers by monodromy vectors, and show how to determine from the monodromy vector the Veech group of the corresponding cover. This is based on joint work with Mauro Artigiani, Chandrika Sadanand, Ferrán Valdez, and Gabriela Weitze-Schmithüsen.
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