The APDE seminar on Monday, 10/21 will be given by Benjamin Küster in Evans 939 from 4:10 to 5pm.
Title: Pollicott-Ruelle resonances and Betti numbers
In joint work with Tobias Weich, we study the multiplicity of
the Pollicott-Ruelle resonance 0 of the Lie derivative along the
geodesic vector field on the cosphere bundle of a closed negatively
curved Riemannian manifold, acting on flow-transversal one-forms. We
prove that if the manifold admits a metric of constant negative
curvature and the Riemannian metric is close to such a constant
curvature metric, then the considered resonance multiplicity agrees with
the first Betti number of the manifold, provided the latter does not
have dimension 3. In dimension 3 and for constant curvature, it turns
out that the resonance multiplicity is twice the first Betti number.