Seminars & Colloquia Calendar

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Convergence of unitary representations and spectral gaps of manifolds

Michael Magee (Durham U. and IAS)

Location:  Hill 705
Date & time: Wednesday, 29 November 2023 at 3:30PM - 4:30PM

Michael Magee (Durham U. and IAS)
Title: Convergence of unitary representations and spectral gaps of manifolds
Abstract:  Let M be a locally symmetric space. I'll discuss the notion of `strong convergence' of a sequence of finite dimensional unitary representations of the fundamental group of M. Once this convergence property is established for particular sequences of representations, it can be used to deduce information about the spectral gap of the Laplacian on covering spaces  of M, or on vector bundles over M. This has led to several recent advances. For example, it is now known that every compact hyperbolic surface has a sequence of covering spaces with asymptotically optimal relative spectral gap. I'll discuss what is known and conjectured for higher dimensional hyperbolic manifolds.

Based on joint works with W. Hide, L. Louder, D. Puder,  J. Thomas.

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