Dynamical zeta functions, Nielsen-Reidemeister theory and Gauss congruences

The study of dynamical zeta functions is a part of the theory of
dynamical systems, but it also intimately related to algebraic geometry,
number theory, topology and statistical mechanics.
In the talk I will discuss the Reidemeister and Nielsen zeta functions.
These zeta functions count periodic points of dynamical system in the
presence of the fundamental group and give  rise to the Reidemeister torsion.
The study of these zeta functions  leads to  a  generalisation to infinite groups
of the classical Burnside-Frobenius  theorem, to the discovery of the groups
with  the property $ R_{\infty}$ and to the Gauss congruences for Reidemeister
and Nielsen numbers.
In the talk a categorification   of dynamical zeta functions via periodic Floer  homology will be proposed.