Title: Equidistribution of the image in the torus of sparse points on dilating analytic curves

Abstract: It is known that under mild assumptions, the image in the d-torus of dilating analytic curves in RdRdR^d equidistributes. I will discuss a sparse version of this phenomenon. As a particular example, let {rnrnr_n} be a sequence of radii, fix an angle in the unit circle and consider the uniform probability counting measures supported on the projection to the 2-torus of the n'th roots of unity in the plane dilated by a factor of rnrnr_n and rotated by this angle. I will talk about the following three types of results:
1. If rnrn