Homogeneous dynamics is the study of asymptotic properties of actions of subgroups of Lie groups on associated homogeneous spaces, including many geometric examples such as Anosov diffeomorphisms of the torus or geodesic flows on negatively curved manifolds. The theory has also deep connections with number theory and diophantine approximations, as shown by Margulis’ proof of Oppenheim conjecture and, more recently, the work of Einsiedler, Katok and Lindenstrauss on Littlewood conjecture.
This workshop will bring together researchers in the domain of homogeneous dynamics and its applications to arithmetic, and will feature the latest developments in the area as well as some mini-courses by some leading experts.
Dense subgroups in simple groups
Dynamics on homogeneous spaces and Diophantine approximation.
Dynamics on quotients of SL(2,C) by discrete subgroups.
Variance estimates on spaces of lattices
Exponents of Diophantine approximation
Approximation diophantienne sur les variétés
Shrinking targets on homogeneous spaces and improving Dirichlet’s Theorem
Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic
Dynamical approaches to automorphic functions and resonances, and
Generalizing Benoist-Quint to homogeneous spaces of non-lattice type
Random walks on homogeneous spaces and diophantine approximation on fractals