IGA/AMSI Workshop

Group-valued moment maps
with applications to mathematics and physics

5-9 September 2011



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

Conference Poster

Lecture Series by Eckhard Meinrenken (University of Toronto)

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.


    Invited Speakers

    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


    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. For a list of budget hotels in Adelaide, please click here.

    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.


    Local Information for Visitors

  • Destination Adelaide (Lonely Planet)
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    • Organisers

    Craig Westerland
    Department of Mathematics and Statistics
    University of Melbourne
    Parkville VIC 3010, Australia

    Phone: (03) 8344 9712
    Fax: (03) 8344 4599
    E-mail: c.westerland@ms.unimelb.edu.au     		Mathai Varghese
    School of Mathematical Sciences
    University of Adelaide
    North Terrace, Adelaide, SA 5005

    Phone: (08) 8303 4173
    Fax: (08) 8303 3696
    E-mail: mathai.varghese@adelaide.edu.au     		Snigdhayan Mahanta
    School of Mathematical Sciences
    University of Adelaide
    North Terrace, Adelaide, SA 5005

    Phone: (08) 8303 1604
    Fax: (08) 8303 3696
    E-mail: snigdhayan.mahanta@adelaide.edu.au     		Pedram Hekmati
    School of Mathematical Sciences
    University of Adelaide
    North Terrace, Adelaide, SA 5005

    Phone: (08) 8303 5261
    Fax: (08) 8303 3696
    E-mail: pedram.hekmati@adelaide.edu.au


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