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December 24, 2005

Winter School on Elliptic Objects

Posted by Urs Schreiber

Next February there is an entire winter school all about Stolz & Teichner’s work on elliptic objects.

From Field Theories to Elliptic Objects
Schloss Mickeln, Düsseldorf (Germany)
February 28 - March 4, 2006
Graduiertenkolleg 1150: Homotopy and Cohomology
Prof. Dr. G. Laures, Universität Bochum
Dr. E. Markert, Universität Bonn
Details : study program
Announcement and Application

Unfortunately, application deadline was already Dec. 15. Too bad. If anyone knows anything about this, please let me know.


In the past two decades mathematicians started to investigate the geometric properties of manifolds by looking at their ambient loop spaces. The stimulation came from particle physists who analyzed these infinite dimensional objects heuristically. The results are very mystifying since they connect physics and differential topology with the theory of elliptic curves and modular forms.

An explanation is expected to come from a new cohomology theory which should be regarded as a higher version of topological K-theory. Such a theory can be obtained by methods of algebraic topology but its relation to loop spaces and field theories is still unclear.

Graeme Segal and Dan Quillen gave a first description of the elements in this new theory in terms of field theories. Later their approach was modified and improved by Stefan Stolz and Peter Teichner. The seminar gives an overview of their work while mainly focusing on the relationship between 1-dimensional euclidean field theories and classical K-theory which is now understood.

Posted at December 24, 2005 1:05 PM UTC

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Re: Winter School on Elliptic Objects

Hallo, Urs!

In case you don’t already know, I remembered that John (Baez) has written something on Elliptic Cohomology in his twf’s. I went back and read it again (when it was originally written I was an undergrad and had no chance to gasp the meaning of anything - I don’t claim things have gotten much better since).

you can find a generel introduction to general homology theory in week 149 and 150, a little bit concerning elliptic cohomology in week 153 and more in 197.


Posted by: Florian on January 16, 2006 8:42 PM | Permalink | Reply to this

Re: Winter School on Elliptic Objects

Hallo Florian,

thanks for your message!

I am aware of these TWFs, but I don’t feel I really understand much about elliptic cohomology yet. With a little luck this will change some day. I was lucky enough to be accepted for the above mentioned winter school, even though I applied well after deadline had passed.

My motivation for being interested in ‘enriched elliptic objects’ is mainly the aspect of describing CFT by means of 2-functors. I think there is something hidden there, and if it happens to be related to elliptic cohomology, all the better. :-)

Posted by: Urs on January 17, 2006 10:14 AM | Permalink | Reply to this
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