Séminaire - Novembre
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: novembre.pdf.
- 05/11/2025 - Florent Ygouf (Université de Rennes)
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: The
horocycle flow in the moduli space of translation surfaces.
Resumé: The
group \(SL(2,\mathbb{R})\) acts on the moduli space of translation
surfaces. The “magic wand” theorem of Eskin,
Mirzakhani, and Mohammadi (~2015) states, in particular, that the
closed sets invariant under this action are holomorphic subvarieties.
The action of the unipotent upper-triangular subgroup is known as the
horocycle flow, by analogy with the horocycle flow on hyperbolic
surfaces. One can think of it as a non-homogeneous analogue of
unipotent flows, whose dynamics were described by the work of Ratner
(~1990). What do the closed invariant sets of the horocycle flow look
like? I will discuss some recent work that addresses this question.