# Orbit of the Diagonal of a Power of a Nilmanifold

 ANALYSIS SEMINAR Topic: Orbit of the Diagonal of a Power of a Nilmanifold Speaker: Alexander Leibman Affiliation: Ohio State University Date: Wednesday, February 27 Time/Room: 2:00pm - 3:00pm/S-101

Let p_1,...,p_k be integer polynomials of one or several variables. There is a relation between the density of polynomial configurations a+p_1(n),...,a+p_k(n) in sets of integers and the form of the closure of the diagonal of X^k under the "polynomial action" (T^{p_1},...,T^{p_k}), where X is a "universal" nilmanifold (that is, a compact homogeneous space of a "universal" nilpotent Lie group) and T is a translation of X . It is easy to describe this diagonal in the case all p_i are linear, and not easy when p_i are not linear.