Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, November 12, 2012

Schreiber 006, 12:15

Amos Nevo


Diophantine approximation, arithmetic groups, and ergodic theory

One of the main goals of classical metric Diophantine approximation is to
quantify the denseness of the rational numbers in the real numbers, or more generally,
of Q^d in R^d. An equally natural problem is to quantify the denseness of the
rational points on the sphere, and more generally, rational points in other
compact and non-compact algebraic sub-varieties in R^d. We will describe a
solution to this problem for a large class of homogeneous varieties. The method
we use is based on a general quantitative duality principle in homogeneous
dynamics that we develop, and on spectral estimates of ergodic averages using
the theory of automorphic forms.
Based on joint work with Alex Gorodnik, and on joint work with Anish Ghosh and
Alex Gorodnik.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006