Growth of cohomology in towers of manifolds: a topological application of the Langlands program

How does the dimension of the first cohomology grow in a tower of covering spaces? After a tour of examples of behaviors for low-dimensional spaces, I will focus on arithmetic manifolds. Specifically, for towers of complex hyperbolic manifolds, I will describe how to bound the rates of growth using results from Langlands functoriality.


Member, School of Mathematics