School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

Technion

One of the main goals of classical metric Diophantine approximation is to

Abstract:

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