Limits of canonical metrics in low-dimensions

Abstract: For a tower of finite normal covers of graphs or surfaces, one can consider a sequence of metrics on the base given by pull-back of canonical metrc of the covers. We show that such a sequence has a limit and it depends only on the cover approximated by the tower up to scaling. The case of compact Riemann surface where the tower approximates the universal cover is due to Kazhdan. In this talk, we will mostly focus on the surface case and explain how the L^2-theory can be applied. This talk is based on a joint work with Farbod Shokrieh and Chenxi Wu.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

2021 Pacific Rim Complex & Symplectic Geometry Conference