Group-valued moment maps
with applications to mathematics and physics
5-9 September 2011
Conference Room 7.15, Level 7, Innova 21 building
(see on the map
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.
David Baraglia (Australian National University)
Keith Hannabuss (University of Oxford)
John Huerta (Australian National University)
Paul Sobaje (University of Melbourne)
Stephan Tillmann (University of Queensland)
Craig Westerland (University of Melbourne)
Ruibin Zhang (University of Sydney)
Titles and Abstracts
Schedule and Slides
List of Participants
Group photo 1
Group photo 2
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:
Position and Affiliation
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.
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.
Participants, other than the invited speakers, are asked to make their own travel and accommodation arrangements. For a list of budget hotels in Adelaide, please click here.
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