# Geometry Seminar

Horospherical measures in the moduli space of abelian differentials (SPECIAL TIME noon-1pm)

Friday, March 12, 2021

12:00-1:00 PM

Off Campus Location

SPECIAL TIME noon-1pm

The classification of horocycle invariant measures on finite volume hyperbolic surfaces with negative curvature is known since the work of Furstenberg and Dani in the seventies: they are either the Haar measure or are supported on periodic orbits. This problem fits inside the more general problem of the classification of horospherical measures in finite volume homogenous spaces.

In this talk, I will explain how similar questions arise in the moduli space of abelian differentials (and more generally in any affine invariant manifolds) and will discuss the definition of horospherical measures in that context. I will then report on progress toward a classification of those horospherical measures that settles the case of « saddle connection free » measures. This is a joint work with J. Smillie, P. Smillie and B. Weiss. Speaker(s): Florent Ygouf (Tel Aviv University)

The classification of horocycle invariant measures on finite volume hyperbolic surfaces with negative curvature is known since the work of Furstenberg and Dani in the seventies: they are either the Haar measure or are supported on periodic orbits. This problem fits inside the more general problem of the classification of horospherical measures in finite volume homogenous spaces.

In this talk, I will explain how similar questions arise in the moduli space of abelian differentials (and more generally in any affine invariant manifolds) and will discuss the definition of horospherical measures in that context. I will then report on progress toward a classification of those horospherical measures that settles the case of « saddle connection free » measures. This is a joint work with J. Smillie, P. Smillie and B. Weiss. Speaker(s): Florent Ygouf (Tel Aviv University)

Building: | Off Campus Location |
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Location: | Virtual |

Event Type: | Workshop / Seminar |

Tags: | Mathematics |

Source: | Happening @ Michigan from Department of Mathematics |