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.