Séminaire - Juin
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger le programme du mois: juin.pdf.
- 28/06/2017 - Simion Filip (Harvard University) - salle 201
Titre: Finiteness
results for orbit closures in the moduli space of flat surfaces
Resumé:The group \(SL(2,\mathbb{R})\) acts on the moduli space of Riemann
surfaces equipped with a holomorphic 1-form. This action can be viewed
as the renormalization of flows on fixed surfaces and understanding the
\(SL(2,\mathbb{R})\)-action on the moduli space has many consequences
for dynamics on individual surfaces. Eskin, Mirzakhani, and Mohammadi
established topological and measure rigidity results in this setting,
analogous to Ratner's results in the homogeneous setting. In joint work
with Eskin and Wright, we established some general finiteness results
for possible orbit closures, which can be summarized as "In a fixed
genus, there are only finitely many unexpected orbit closures". After
providing some background, I will explain the result in more detail and
describe the techniques.