Exposé d'Antoine Derimay

Poisson boundaries: discretization and rigidity
Poisson boundaries are a measure theoretic object associated to a random walk, encompassing both the long-term behaviour of the walk and the bounded harmonic functions. When the random walk is on a group that group acts on its Poisson boundary, in a very nice way. In fact, following the work of Bader and Furman, a good description of the Poisson boundary of a group can lead to numerous rigidity properties of that group.
If there is time, I will then briefly explain how to obtain descriptions of some Poisson boundaries using discretization procedures.

Exposé de Louis-Brahim Beaufort

Ergodicity and rigidity for frame flows in negative curvature
The frame flow is obtained by parallel transporting frames along the geodesic flow. When the underlying space is negatively curved, the geodesic flow exhibits hyperbolicity properties, and the frame flow inherits a partially hyperbolic structure. In this short talk, I will explain how classical tools of differential geometry, such as connections, holonomy, and curvature, can be applied to investigate dynamical questions, specifically the ergodicity and regularity of the partially hyperbolic decomposition of the frame flow.