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SUMMARY:The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
  - Gabriel Paternain (Cambridge)
DTSTART:20220511T150000Z
DTEND:20220511T160000Z
UID:TALK173858@talks.cam.ac.uk
CONTACT:Henry Wilton
DESCRIPTION:The Ruelle zeta function is a natural function associated to t
 he lengths of the closed geodesics of a closed negatively curved manifold\
 , and it is known to have a meromorphic extension to the whole complex pla
 ne. In this talk I will explain the main ideas that go into the proof of t
 he following result: for a generic conformal metric perturbation of a hype
 rbolic 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).\n\nThis is joint work with Mi
 hajlo Cekić\, Benjamin Delarue and Semyon Dyatlov
LOCATION:MR13
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