Workshop: Dirac Operators in Geometry, Topology, Representation Theory, and Physics

Lectures Series by Dan Freed (University of Texas, Austin)

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Abstract

Dirac introduced his eponymous operator to describe electrons in quantum theory. It was rediscovered by Atiyah and Singer in their study of the index problem on manifolds. In these lectures we explore new theorems and applications. Several of these also involve K-theory in its recent twisted and differential variations.

Titles of individual lectures

• Loop groups and Dirac families

I will describe the finite and infinite-dimensional versions of the construction which yields my theorem with Hopkins and Teleman. This will include some generalities about loop groups and their representations.

• Introduction to twisted K-theory

After a review of standard K-theory I will discuss the twisted form and some properties. Then I will compute twisted K_G(G) in some cases.

• A TQFT from twisted K-theory

I will discuss TQFTs in general and give some examples, etc. I will show how to construct the ring structure on twisted K_G(G).

• Differential K-theory and the Atiyah-Singer theorem

An introductory lecture on differential cohomology theories in general and differential K-theory in particular. Then the differential index theorem with Lott.

• Anomalies and "categorified" index theorems

A general lecture on some physics, then some discussion of anomalies in supersymmetric quantum mechanics and on the worldsheet of string theory.

Downloads

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Schedule and slides

Participant information

Venue

Conference Room 7.15, Level 7, Innova 21 building (see on the map).

Registration

There will be no registration fees: all are welcome. However, if you are interested in attending, kindly send an e-mail to Snigdhayan Mahanta by 17 September 2010, with the following information:

• Name
• Position and Affiliation
• E-mail

Please also indicate in your e-mail whether you would like to attend the workshop dinner (Tuesday evening, 19 Oct), which will be $5 per person.

Funding

This event is co-sponsored by the Australian Mathematical Sciences Institute (AMSI). AMSI allocates a travel allowance to each of its member universities (for a list of members, click here). Students or Early Career Researchers from AMSI member universities without access to a suitable research grant or other source of funding may apply to their Head of Mathematical Sciences for subsidy of travel and accommodation out of the departmental travel allowance. No other funding is available.

Accommodation

Participants, other than the invited speakers, are asked to make their own travel and accommodation arrangements.

Internet access

The University of Adelaide provides wireless access for visitors whose home institutions have eduroam. For more information on how to set up eduroam, please click here.

Organisers

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