A famous conjecture of Alon stated that for fixed d, random d-regular graphs on a large number of vertices have almost optimal spectral gap between the two largest eigenvalues of the adjacency operator. Friedman proved this conjecture in 2008. Friedman also broadened the conjecture to random large-degree covering spaces of a fixed finite base graph. This more general conjecture was recently proved by Bordenave and Collins. We have proved an analog of these conjectures for random infinite area hyperbolic surfaces without cusps. The spectral theory here is interesting; we obtain almost optimal spectral gap results for objects called resonances that generalize eigenvalues of the Laplacian but can be much more subtle.

I'll give some ideas of the proof in the talk.

(This is joint work with F. Naud)

Alexander Murray Wright is inviting you to a scheduled Zoom meeting.

Topic: Geometry Seminar
Time: Jul 12, 2021 09:30 AM America/Detroit

Join Zoom Meeting
https://umich.zoom.us/j/91763608340?pwd=S25pdUNyTFBwdGVDaUhNd0pFcXFZQT09

Meeting ID: 917 6360 8340
Passcode: 859275



Speaker(s): Michael Magee (Durham University)