**Amos Nevo**

Technion-Israel Institute of Technology

February 11, 2016

**Arithmetic groups, the automorphic representation, and intrinsic Diophantine approximation**:
We will describe a recently developed general approach to Diophantine
approximation on homogeneous algebraic varieties, and demonstrate it in some familiar natural examples. The approach utilizes harmonic analysis in the automorphic representation of semisimple algebraic groups and some arguments in homogeneous dynamics and ergodic theory. It provides the best possible solution to a host of intrinsic Diophantine approximation problems which were not accessible by previous techniques.
Based on joint work with Anish Ghosh and Alex Gorodnik.