On the Calegari-Emerton conjectures for abelian type Shimura varieties

Emerton’s completed cohomology gives, at present, the most general notion of a space of p-adic automorphic forms. Important properties of completed cohomology, such as its ‘size’, is predicted by a conjecture of Calegari and Emerton, which may be viewed as a non-abelian generalization of the Leopoldt conjecture. I will discuss the proof of many new cases of this conjecture, using a mixture of techniques from p-adic and real geometry. This is joint work with David Hansen.

Zoom: https://harvard.zoom.us/j/99334398740

Password: The order of the permutation group on 9 elements.