The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds

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• Gabriel Paternain (Cambridge)
• Wednesday 11 May 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Henry Wilton.

The Ruelle zeta function is a natural function associated to the lengths of the closed geodesics of a closed negatively curved manifold, and it is known to have a meromorphic extension to the whole complex plane. In this talk I will explain the main ideas that go into the proof of the following result: for a generic conformal metric perturbation of a hyperbolic 3-manifold, the order of vanishing of the Ruelle zeta function at zero equals $4-b_1$, contrary to the hyperbolic case where it is equal to $4-2b_1$ ($b_1$ is the first Betti number).

This is joint work with Mihajlo Cekić, Benjamin Delarue and Semyon Dyatlov

This talk is part of the Differential Geometry and Topology Seminar series.

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