Negatively curved manifolds, Betti Numbers, and Singer Conjecture

Abstract: The study of negatively curved manifolds is at the crossroads of modern geometry and topology. In this talk, I will present new ideas and techniques for studying the cohomology of such manifolds. More precisely, I will discuss the asymptotic growth rate of Betti numbers in towers of hyperbolic manifolds, and general vanishing results for Atiyah’s L2-Betti numbers. Finally, I will explain the connection between such results and the longstanding Singer’s conjecture. This is an overview of two joint projects with M. Stern.