I will present a new explanation of the connection between the fractal
uncertainty principle (FUP) 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. The talk will assume
no knowledge of the subject and I will also present applications of
FUP to properties of eigenfunction on compact hyperbolic surfaces due
to Dyatlov-Jin.

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