This book presents an overview of different ongoing research directions centred around the main theme: traces, determinants and their zeta functions. The collection of papers in the book arises from an activity held at the Max-Planck Institute for Mathematics in Bonn in the autumn of 2005. The authors discuss many topics, including traces in number theory, traces in dynamical systems (based on the Ruelle zeta function and its generalisation), traces in non-commutative geometry (ranging from spectral triples for III-factors and non-commutative geometry on trees and buildings to quantum groups), traces on pseudo-differential operators and associated invariants of underlying manifolds (e.g. invariants of CR manifolds produced by non-commutative residue or defect formulas and zeta values for boundary valued problems) and gauge fields and quantum field theory (in particular analysis of the Schwinger-Dyson equation in perturbative quantum field theory or various applications in QCD and interacting particle systems).

Reviewer:

pso