Séminaire - Avril
Le séminaire aura lieu un mercredi du mois (exceptionnellement deux exposés) de 14h à 15h et 15h30 à 16h30 à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: avril.pdf.
- 30/04/2025 - David Aulicino (Brooklyn College)
- 30/04/2025 - Anja Randecker (Saarland University, Heidelberg University)
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: Siegel-Veech
Constants of Cyclic Covers of Generic Translation Surfaces
Resumé: 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 and a connection to combinatorics will be
presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick
Salter, and Martin Schmoll.
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: Free
groups as Veech groups of finite-area translation surfaces
Resumé: 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.