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.