Mini-Workshop: Zeta Functions, Index and Twisted K-Theory; Interactions with Physics

Abstract

This mini-workshop brought together number theorists, analysts, geometers and mathematical physicists to discuss current issues at the common boundary of mathematics and physics. Topics covered included the number theoretic and algebraic structures underlying renormalization, twisted K-theory and higher algebraic structures, modular forms, and arithmetic and spectral zeta functions. A particular theme was around developing interconnections between arithmetic (multiple) zeta functions, spectral zeta functions associated with elliptic operators (and related spectral invariants such as spectral flow) and current issues in physics such as renormalization and mirror symmetry. Multiple zeta functions appear in index theory and $K$-theory via their relation to anomalies, in number theory in their relation to polylogarithms, in renormalization questions in perturbative quantum field theory and Hopf algebras, in duality issues and in twisted $K$-theory for index theorems for projective families of elliptic operators, thereby providing a rich set of overlapping topics with common analytical issues.

This meeting was organized around one hour talks, four each day, with plenty of time between talks for informal discussion and a 45 minute talk in the afternoon for students; three graduate students were among the 16 participants. Some participants lectured for two hours in order to have time to introduce the audience to the subject before entering the technical details.

The organizers and participants would like to thank the Mathematisches Forschungsinstitut Oberwolfach for providing a pleasant and stimulating enviroment for this meeting.