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Seminar

GAAHD Research Seminar: Critical exponents, regular covers and amenability March 17, 2015 (10:30 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Richard Sharp (University of Warwick)
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A beautiful theorem of Brooks says that, for a wide class of Riemannian manifolds, the bottom of the spectrum of the Laplacian on a regular cover is equal to the bottom of the spectrum of the base if and only if the covering group is amenable. In the case where the base manifold is a quotient of a simply connected manifold with pinched negative curvatures by a convex co-compact group, we will give a analogous results for critical exponents and for the growth of closed geodesics. This is joint work with Rhiannon Dougall.

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