Analysis and PDE Seminar: Fractal uncertainty for transfer operators

Seminar | October 16 | 4:10-5 p.m. | 740 Evans Hall

 Maciej Zworski, UC Berkeley

 Department of Mathematics

I will present a new explanation of the connection between the fractal uncertainty principle of Bourgain–Dyatlov, a statement in harmonic analysis, and the existence of zero free strips for Selberg zeta functions, which is a statement in geometric scattering/dynamical systems. The connection is proved using (relatively) elementary methods via the Ruelle transfer operator which is a well known object in thermodynamical formalism of chaotic dynamics. (Joint work with S Dyatlov.)