The n-Category Café

ESI Program K-Theory and Quantum Fields

Posted by Urs Schreiber

This summer in Vienna at ESI takes place a program titled

K-Theory and Quantum Fields

May 21 - July 27, 2012 (webpage)

organized by Matt Ando, Alan Carey, Harald Grosse and Jouko Mickelsson.

It starts out with

• introductory instructional lectures in the week May 28-June 1;

• advanced instructional lectures in the week June 4- June 8.

Details should appear by beginning of March on the webpage. As far as I am aware, the following speakers and topics are expected for the instructional lectures.

• John Francis: factorization algebras/homology;
• Dan Freed (probably on June 7th and 8th, topic to be announced);
• Mathai Varghese: T-duality and K-theory;
• Frederic Rochon: introduction to K-theory;
• myself: twisted differential structures in string theory;
• Danny Stevenson: twisted K-theory, higher structures;
• Bai-Ling Wang: K-theory, K-homology and twisted geometric cycles.

I’ll post an alert in the comments below as soon as there is more information available.

From the program webpage:

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.