## February 22, 2012

### 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.

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.

Posted at February 22, 2012 8:44 PM UTC

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### Re: ESI Program K-Theory and Quantum Fields

Most abstracts are now available: here.

Posted by: Urs Schreiber on March 26, 2012 8:29 AM | Permalink | Reply to this
Weblog: The n-Category Café
Excerpt: A preview of an article on principal bundles in higher geometry.
Tracked: April 23, 2012 11:00 PM

### Re: ESI Program K-Theory and Quantum Fields

I am preparing some notes to go with my lectures, on the $n$Lab at:

twisted smooth cohomology in string theory

The idea of the first session tomorrow is to exhibit the general pattern by way of a familiar class of examples, viewed from a new angle:

reduction of structure groups, vielbein fields, generalized geometry and exceptional geometry, all regarded as special cases of twisted smooth cohomology in low degree.

The remainder of the entry is currently still mostly skeletal. Will be expanded in the next days, as I go along.

Posted by: Urs Schreiber on May 28, 2012 10:58 PM | Permalink | Reply to this

### Re: ESI Program K-Theory and Quantum Fields

There are now, I think, fairly stable notes on the five sessions of lecture that I gave:

If you spot any typos (or errors), I’d be grateful to hear about them!

Coming Wednesday this is to be rounded up with a research-level talk on

Posted by: Urs Schreiber on June 6, 2012 5:44 PM | Permalink | Reply to this

### Re: ESI Program K-Theory and Quantum Fields

Dan Freed has now made available a supplementary text to go along with his lectures at ESI last week:

• Dan Freed, Lectures on twisted K-theory and orientifolds (pdf)
Posted by: Urs Schreiber on June 15, 2012 5:29 PM | Permalink | Reply to this

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