# Dynamics seminar: Nadav Yesha (Kings College): Pair correlation for quadratic polynomials mod 1

It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. We provide explicit Diophantine conditions on the coefficients of degree 2 polynomials under which the limit of an averaged pair correlation density is consistent with the Poisson distribution, using a recent effective Ratner equidistribution result on the space of affine lattices due to Strömbergsson. This is joint work with Jens Marklof.

## Date:

Tue, 21/03/2017 - 14:00 to 15:00