Orateur
Polyxeni Spilioti
Description
In this mini course, we will introduce the dynamical zeta functions of Ruelle and Selberg for hyperbolic manifolds or more generally for locally symmetric spaces of rank one.
We will present the so called Fried 's conjecture, i.e., a conjectural equality between the Ruelle zeta function at zero and a spectral invariant, the analytic torsion. In the second part of the mini course, we will talk about this problem, in the setting of a non-unitary representation of the lattice we consider. We will see how one can use the trace formula to study this problem and also we will present the definition of the refined analytic torsion and the Cappell-Miller torsion. Time depending, we will discuss some further problems related with these objects.
