Department of Mathematics
Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
Alexander Felshtyn
Boise State University
The study of dynamical zeta functions is part of the theory of dynamical systems, but is 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 systems in the presence of fundamental group. Arithmetical congruences for Reidemeister numbers will be described. I will explain how dynamical zeta functions give rise to the Reidemeister torsion. This is an important topological invariant, which has useful applications in topology, quantum field theory and dynamical systems. The connection between symplectic Floer homology for surfaces and Nielsen fixed point theory will be described.
All interested persons are welcome.