Monday 12th of May 2025, 13:30-14:30 in HG03.082
Chris Pirie
Zeta Functions, Dynamics, and the Fried Conjecture
Zeta functions are functions which can be viewed as encoding information or mathematical data, the canonical example being the relation between the Riemann zeta function and prime numbers. In this talk, we present a dynamical zeta function, called the Ruelle zeta function, which encodes information about the periodic orbits of the dynamical system. We provide an example of this zeta function in the case of suspension flow of a diffeomorphism, and we will also discuss the associated Fried conjecture, relating the value at 0 for the Ruelle zeta function to an invariant of the manifold. Time permitting, we also present equivariant versions for the Ruelle zeta function and Fried conjecture for compact group actions.