Spectrum and growth on infinite covers
Time and place
12:30–1:30 PM on Tuesday, November 18th, 2025; MR 418N
Richard Sharp (University of Warwick)
Note
Note that we meet in the Physics Colloquium room. Please respect the space.
Abstract
It is easy to see that zero is an eigenvalue of the Laplacian on a compact manifold. If one takes an infinite cover of the manifold, is zero still in the spectrum? This question turns out to have a nice answer, known since the 1980s, which is related to the Banach—Tarski Paradox. We will discuss this and a related dynamical problem. In the latter case, we have a new result which describes what happens when a crucial symmetry assumption is dropped – this is joint work with Rhiannon Dougall.
