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Distinct distances on surfaces arising from cofinite Fuchsian groups

  • 演讲者:孟宪昌(哥廷根大学)

  • 时间:2021-05-26 20:00-21:00

  • 地点: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.