Schedule, Notes/Handouts & Videos

We give an introduction to the Weyl chamber flow for a compact locally symmetric manifold. We describe some of its dynamical properties and explain two recent geometric applications.

I will outline some of the ideas behind the developments in ergodic theory and combinatorial number theory starting with Szemeredi's theorem on arithmetic progressions in dense subsets of the integers and its ergodic theoretic proof by Furstenberg, and culminating with the recent proof of the Hardy-Littlewood estimates for the number of solutions to systems of linear equations of finite complexity.

I will present   equidistribution results for the horocyclic flow, and the strategy of the proofs, involving the dynamical properties of the geodesic flow, and a theorem of unique ergodicity of the horocyclic flow due to Burger and Roblin.