# Kazhdan's Theorem for Metric Graphs

## Chenxi Wu, Rutgers University

## Date and time: 2pm, Friday, October 4, 2019

## Place: CUNY Graduate Center, Rm 5383

There is an analogy between the study of metric graphs and the study
of Riemann surfaces, and a question is to construct uniformization
theorem for metric graphs which would require a concept of "hyperbolic
metric" on it. With Farbod Shokrieh, we found a graph theoretic
analogy of a classical result by Kazhdan on the limit of canonical, or
Bergman metric under a tower of normal covers, which indicates that
the limiting metric might be such a candidate. I will also discuss
generalizations of it to higher dimensional simplicial complex and
some further questions.