Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Extending weakly polynomial functions from high rank varieties

Prof. Dr. Tamar Ziegler talk

**Date:** 21.11.18 **Time:** 15.45 - 16.45 **Room:** ETH HG G 43

Let k be a field, V a k-vector space, X in V a subset. Say that f: X —> k is weakly polynomial of degree a if its restriction to any isotropic subspace is a polynomial degree of a. We show that if X is a high rank variety then any weakly polynomial function of degree a is the restriction to X of a polynomial of degree a on V. Equidistribution properties of high rank polynomials play an important role. Joint work with D. Kazhdan.