The study of Ergodic Theory and dynamics of group actions and its interactions with number theory is an extremely active field of research. The recent important work of Einsiedler-Katok-Lindenstrass on the Littlewood conjecture in Diophantine approximation and Tao-Green on primes in arithmetics progressions offer spectacular instances of the effectiveness of dynamical and ergodic techniques. The project aims to study number theoretic properties of manifold on the one hand and develop a new set of tools in the study of dynamical systems on the other. The problems addressed are at the forefront of research in this exciting interdisciplinary area. The method used to study the key problems will involve a combination of creative applications of existing methods and the development of a new set of tools to address long standing problems.
