Event № 792
In this talk I will present a generalization of the Euclidean lattice point counting problem in the context of a certain type of homogeneous groups, the so-called Heisenberg groups. This problem was first considered in a paper by Garg, Nevo & Taylor, in which various upper bounds for the lattice point discrepancy were obtained with respect to a certain family of homogeneous norms. In the case of the first Heisenberg group, we will show that the upper bounds obtained by Garg, Nevo & Taylor are sharp when the norm under consideration is the Cygan-Koranyi norm, and I will present the main ideas needed for the proof. If time permits, I will present some recently obtained results regarding the higher dimensional case.