Generalized polynomials, recurrence, uniform distribution and translations on nil-manifolds

Vitaly Bergelson, Ohio State Univ.

"Generalized polynomials" are functions which are obtained from the conventional polynomials by the use of the greatest integer function, addition and multiplication. They appear naturally in various mathematical contexts including symbolic dynamics, the theory of mathematical games, number theory and combinatorics. We will discuss the recently established connection between the generalized polynomials and dynamical systems on nil-manifolds and the ensuing applications to uniform distribution and ergodic Ramsey theory.