Full Description
Traces and determinants arise in various guises in many areas of mathematics and mathematical physics: in regularization procedures in quantum fields theory, in the definition of correlation functions and partition functions, in index theory for manifolds and for noncommutative spaces, and in the study of dynamical systems, through zeta functions and zeta determinants, as well as in number theory in the study of zeta and L-functions. This volumes shows, through a series of concrete example, specific results as well as broad overviews, how similar methods based on traces and determinants arise in different perspectives in the fields of number theory, dynamical systems, noncommutative geometry, differential geometry and quantum field theory.
Contents
Number theory, dynamical systems, noncommutative geometry, differential geometry and quantum field theory are five areas of mathematics represented in this volume, which presents an overview of different ongoing research directions around the main theme of traces and zeta functions. This collection of articles arises from an activity that took place at the Max-Planck Institute for Mathematics in Bonn.
