Dynamical systems seminar: Closed geodesics in dilation surfaces

Speaker: Guillaume Tahar (BIMSA)

Abstact: Dilation surfaces are generalizations of translation surfaces in which the transition maps are translations and homotheties. Their directional dynamics exhibit new behaviors, such as trajectories accumulating on limit cycles or Cantor sets. A now-classical theorem proves the existence of closed geodesics on any translation surface. We will outline the proof given by Masur and Smillie. In recent work, in collaboration with Adrien Boulanger and Selim Ghazouani, we prove the analogous theorem for dilation surfaces. The proof involves a partial compactification of the moduli space of dilation surfaces, accounting for various types of degenerations. If time permits, we will discuss a conjecture providing a strong version of the existence theorem for closed geodesics.

Time: 16:00, Thur., Nov. 21, 2024

Location: Online
Microsoft Teams Meeting ID: 954 585 487 551 9 (Passcode: tzAM9w)