**Title:** On the image in the torus of sparse points on expanding analytic curves

**Speaker:** Michael Bersudsky (OSU)

**Abstract:** It is known that the projection to the 2-torus of the normalised parameter measure on a circle of radius R in the plane becomes uniformly distributed as R grows to infinity. I will discuss the following natural discrete analogue for this problem. Starting from an angle and a sequence of radii {Rn} which diverges to infinity, I will consider the projection to the 2-torus of the n’th roots of unity rotated by this angle and dilated by a factor of Rn. The interesting regime in this problem is when Rn is much larger than n so that the dilated roots of unity appear sparsely on the dilated circle.