November 5th, 2021

- Gilles Courtois, Sorbonne Université

- Thi Dang, Heidelberg University

- Thi Hanh Vo, University of Luxembourg

10:00-11:00 | Thi Hanh Vo: Short closed geodesics on cusped hyperbolic surfaces |

11:00-11:30 | Coffee break |

11:30-12:30 | Gilles Courtois: Cheeger type inequality for differential forms |

12:30-14:30 | Lunch |

14:30-15:30 | Thi Dang: Equidistribution and counting of maximal flats |

15:30-16:00 | Tea break |

Gilles Courtois:

On a compact Riemannian manifold, the Cheeger's inequality relates the first non zero eigenvalue of the Laplacian of functions with an isoperimetric constant of the manifold. J. Cheeger asked if an analogous inequality would hold for the first non zero eigenvalue of differential forms. We will discuss the case of 1-differential forms. (Joint work with Adrien Boulanger).

Thi Dang:In this talk, I will present a work in progress with Jialun Li.
Regular Weyl chamber flows of a higher rank symmetric space of non-compact type generalize in a Lie group action sense, the geodesic flow of a hyperbolic surface. For compact hyperbolic surfaces, equidistribution of closed geodesics is due to Bowen and Margulis (1969).

In higher rank and in the compact case, periodic orbits of regular Weyl chamber flow live on tori.
Using orbital counting results of Gorodnik-Nevo (2009) and an adaptation of Roblin's ideas, we obtain an equidistribution result of these tori.

We consider the set of closed geodesics on cusped hyperbolic surfaces. Given any non-negative integer k, we are interested in the set of closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.

The Geometry Day will take place at the Créteil campus of the Laboratoire d'Analyses et de Mathématiques Appliquées. All talks will be in room P2 131 (building P, wing 2, first floor).

To reach the university by public transportation there are multiple options:

- Metro 8, stop Créteil-Université: exit to the right and follow the directions for the university;
- RER D, stop Vert-de-Maisons: take the square Maurice Dufourmantelle, cross rue Jean-Jaures and then follow avenue des Petites Haies;
- Bus 181 or 281, stop Créteil-Université.