Dynamical systems and Diophantine geometry
Supervisor: Alexander Gorodnik
This project lies on the crossroads between dynamical systems and number theory. We will be interested in the structure of the set of integral/rational solutions of a systems of polynomial equations. In many interesting cases the set of solutions is equipped with a group action and one can use techniques from the theory of dynamical systems to analyse this problem.
1. G. Margulis, Diophantine approximation, lattices and flows on homogeneous spaces. A panorama of number theory or the view from Baker's garden (Zurich, 1999), 280-310, Cambridge Univ. Press, Cambridge, 2002.
2. E. Lindenstrauss, Some examples how to use measure classification in number theory. Equidistribution in number theory (A. Granville and Z. Rudnick, eds.), 261-303, Springer, 2007.
3. D. Kleinbock, N. Shah, A. Starkov, Dynamics of subgroup actions on homogeneous spaces of Lie groups and applications to number theory. Handbook of dynamical systems, Vol. 1A, 813-930, North-Holland, Amsterdam, 2002.
4. H. Oh, Orbital counting via mixing and unipotent flows, http://www.math.brown.edu/~heeoh/Ohpisalecture.pdf