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MLA - Resonant spaces at zero for volume-preserving Anosov flows October 29, 2019 (11:00 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Mihajlo Cekic (Max-Planck-Institut für Mathematik)
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Recently Dyatlov and Zworski proved that the order of vanishing of the Ruelle zeta function at zero, for the geodesic flow of a negatively curved surface, is equal to the negative Euler characteristic. They more generally considered contact Anosov flows on 3-manifolds. In this talk, I will discuss an extension of this result to volume-preserving Anosov flows, where new features appear: the winding cycle and the helicity of a vector field. A key question is the (non-)existence of Jordan blocks for one forms and I will give an example where Jordan blocks do appear, as well as describe a resonance splitting phenomenon near contact flows. This is joint work with Gabriel Paternain. 

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