Géométrie et dynamique dans les espaces de modules

Séminaire Mensuel

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.