IGA: Luca di Cerbo - The Singer conjecture in dimension three revisited and its extensions
Channel: UMD Mathematics
Date: 2021-02-18

Abstract: In this talk, I will show how Price inequalities for harmonic forms combined with some standard topology and geometry of 3-manifolds imply the Singer conjecture in dimension three. This provides an alternative proof of a result of Lott and Lueck (Invent. Math., 1995). Finally, I will outline some generalizations of this new approach in higher dimensions. This is part of a joint project with M. Hull and M. Stern.