ESI Program
on
K-Theory and Quantum Fields

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Overview

THIS PAGE IS A PRELIMINARY ANNOUNCEMENT. THE ACTUAL PROGRAM WILL BE POSTED AT

http://www.esi.ac.at/activities/lectures.html

Recent research in quantum field theory, string theory and M-theory has exposed intriguing connections between topology, geometry, analysis and physics. Of interest for this program is the role of K-theory in its various forms: twisted and untwisted, differential, Kasparov's KK, and associated areas such as index theory and higher geometric topological and algebraic structures.

The connections between all of these areas are still evolving. The program will provide instructional lectures for those wishing to learn about all or some of these topics. There will also be two workshops focussing on different aspects of the interactions between these research fields. One of the principal aims of this ESI program is to bring together researchers familiar with different aspects of the current interaction and to expose the area to younger researchers.

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Organisation

There will be one week of introductory instructional lectures for students and postdoctoral fellows. On the first day there will be a tutorial on K-theory for beginners. This will be followed in week 2 by some advanced lectures combined with some research talks. The third week will be the first research workshop.

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Provisional Schedule

Instructional lectures:

May 28: bank holiday, May 29: Schreiber, Rochom, Stevenson, tutorial, May 30: Schreiber, Stevenson, Francis, May 31: Francis, Schreiber, Rochon, Lesch, June 1: Schreiber, Carey, Lesch

June 4: Wang, June 5: Wang, Baum, June 6: Wang, Baum, June 7: Freed, Free afternoon, June 8: Freed, Freed

In addition the first workshop is on the general area of topological field theory scheduled mainly in week 3 (June 11-13), with some talks in the week June 4-8. The second workshop is scheduled for July 16-20, with topics including twisted K-theory, Deligne cohomology, and applications to quantum field theory (D-branes, anomalies). The organisers hope the program will succeed in looking to the future of physics/K-theory interactions.

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Instructional Program (provisional)

J. Francis	Factorisation algebras and homology	Abstract
D. Freed	Twisted K-theory and superstrings	Abstract
V. Mathai	T-Duality and KK-theory	Abstract
F. Rochon	K-duality on stratified spaces	Abstract
U. Schreiber	Twisted differential structures in string theory	Abstract
D. Stevenson	An introduction to twisted K-theory and higher structures	Abstract
B-L Wang	Twisted geometric cycles and twisted K-homology	Abstract

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Discussion

Further details will be posted on this page as they become available.

Possible topics for the Program

In general terms there will be a focus on geometric and topological problems in quantum field theory including string theory and M-theory (D-branes and M-branes) including dualities and their role in string theory. We expect twists in the form of twisted K-theory and higher analogues that may involve other generalised cohomology theories to be discussed. Differential K-theory, both twisted and untwisted and ellipic cohomology are aspects of this. Noncommutative geometry in the form of twisted K-homology both analytic and geometric as well as the use of KK-theory and fractional analytic index theorems are likely topics. Increasingly apparent are the subtleties in the mathematical interpretation of the B-field which is a topic of interest to many participants. Twists other than that of the usual degree three are also proving to be important, as is seen in the description of orientifolds. Elliptic cohomology or TMF have been constructed to explain the elliptic and Witten genera coming from quantum field theories and geometric models for such cohomology theories are a likely topic. String structures or their twisted versions on the loop space are an essential part of this.