Title: Lattice Point Counting: From Gauss Circle Problem to Heisenberg Norms
Speaker: Elizabeth Campolongo - The Ohio State University
Abstract: The question of how many integer lattice points are in, on, and near convex surfaces is a classical problem in number theory and other similar areas of mathematics. We begin this talk with a discussion of the Gauss circle problem. This question has been rephrased over the years and expanded to include other surfaces. We will discuss some of these variants and interesting proof techniques. Our talk concludes with a bound on the number of lattice points on and near a Heisenberg norm ball (B_R^{\alpha,A} := {(z,t) \in Z^{2d} x Z: |z|^\alpha + A|t|^{\alpha/2} \leq R^\alpha}), achieved by defining a measure on a thickened and truncated lattice
