Abelian Livshits Theorem

CDSNS Colloquium
Friday, April 9, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Zoom (see additional notes for link)
Andrey Gogolev – The Ohio State University – gogolyev.1@osu.eduhttps://people.math.osu.edu/gogolyev.1/
Alex Blumenthal

Please Note: Zoom link: https://zoom.us/j/97732215148?pwd=Z0FBNXNFSy9mRUx3UVk4alE4MlRHdz09

The classical Livshits theorem characterizes coboundaries over a transitive Anosov flow as precisely those functions which integrate to zero over all periodic orbits of the flow. I will present a variant of this theorem which uses a weaker assumption and gives a weaker conclusion that the function is an ``abelian coboundary.” Such weaker version corresponds to studying the cohomological equation on infinite abelian covers e.g., for geodesic flows on abelian covers of hyperbolic surfaces. I will also discuss a connection to the marked length spectrum rigidity of Riemannian metrics. Joint work with Federico Rodriguez Hertz.