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The wave trace on asymptotically complex hyperbolic manifolds

Hadrian Quan
Thursday, December 7, 2023 - 2:00pm to 3:00pm
PDL C-38

The behavior of solutions to the wave equation on a Riemannian manifold has a close relationship with both the behavior of geodesics and the spectrum of the Laplacian. In this talk, following Duistermaat-Guillemin, we study the wave solution operator on asymptotically complex hyperbolic manifolds and analyze of its (regularized) trace. On this class of non-compact manifolds, modeled on the complex ball with its Bergman metric, we prove in particular that the leading term arises as a renormalized volume of this non-compact space, and prove a relationship between singularities of the wave trace and the lengths of closed geodesics.

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