2024 Program for Women+ and Mathematics

Abstract: How fast do Betti numbers grow in a congruence tower of covering spaces? I'll discuss this question in the special case of Picard modular surfaces, which are 4-dimensional real manifolds. There, the question is most interesting in degree 1, for which there is expected to be very little cohomology. I’ll explain how the problem is related to automorphic forms, and specifically how the dearth of cohomology classes is a consequence of Langlands functoriality.