Workshop: Group-Valued Moment Maps with Applications to Mathematics and Physics

Lectures Series by Eckhard Meinrenken (University of Toronto)

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Titles of individual lectures

• Introduction to G-valued moment maps

The theory of quasi-Hamiltonian G-spaces with G-valued moment maps has its origins in 2-dimensional gauge theory. Its features are similar to the usual Hamiltonian theory, but with interesting modifications. We will give an overview of the theory, with discussions of a convexity theorem and a Kirwan surjectivity theorem.

• Dirac Geometry and Witten's volume formulas

Dirac geometry treats 2-forms and bivector fields within a common framework. We will explain how this leads to a conceptual approach to G-valued moment maps. As an application, we will construct Liouville volume forms, leading to a proof of Witten's volume formulas for moduli spaces of flat G-bundles over surfaces.

• Dixmier-Douady theory and pre-quantization

Dixmier-Douady bundles provide geometric realizations of integral degree three cohomology classes over a space. We will use these bundles to construct distinguished "twisted Spin-c structures" on quasi-Hamiltonian G-spaces, and also define pre-quantizations in similar terms.

• Quantization of group-valued moment maps

We will review Rosenberg's definition of twisted K-homology in terms of Dixmier-Douady bundles and the Freed-Hopkins-Teleman theorem on the twisted K-homology of Lie groups. We then define the quantization of group-valued moment maps as push-forwards in twisted K-homology.

• Application to Verlinde formulas

The quantization of a quasi-Hamiltonian space is computable via localization. In conjunction with a `quantization commutes with reduction' theorem, this leads to the symplectic version of the Verlinde formulas for moduli spaces of flat G-bundles.

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Schedule and slides

• Conference dinner is on Tuesday, 6 September at 6pm.

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 5 August 2011, 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, 6 September), 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.

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