Research-Distinct distances on surfaces arising from cofinite Fuchsian groups

Research

Algebra & Combinatorics Seminar

Distinct distances on surfaces arising from cofinite Fuchsian groups

Speaker: Xianchang Meng (University of Göttingen)
Time: May 26, 2021, 20:00-21:00
Location: Zoom ID 630 6315 3717, Passcode 210526

Abstract

Erdős (1946) proposed the question of finding the minimal number of distinct distances among any N points in the plane. We consider this problem in hyperbolic surfaces associated with cofinite Fuchsian groups, i.e. the volume of the surface is finite. We prove a lower bound of the same strength as Guth-Katz. In particular, for any finite index subgroup of the modular group, we extract out the dependence of the implied constant on the index.