JournalsowrVol. 1 / No. 2DOI 10.4171/owr/2004/20

Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties

  • Victor W. Guillemin

    Massachusetts Institute of Technology, Cambridge, USA
  • Volker Puppe

    Universität Konstanz, Germany
  • Michèle Vergne

    École Polytechnique, Palaiseau, France
Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties cover

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Abstract

The meeting brought together people with different mathematical background, who all use cohomological methods to study symmetries of manifolds. The main aim was the exchange of ideas, recent results, and the discussion of open problems and questions from diverse viewpoints. % The workshop was organized by % Victor Guillemin (Cambridge, USA), Volker Puppe (Konstanz) % and Mich\`ele Vergne (Palaiseau). Altogether there were 27 talks (including an evening talk on computer programs), and a Hausmusik evening with an artistic juggling intermission. All talks reflected the central theme of the workshop, namely the use of (equivariant) cohomology in studying Lie group actions on manifolds. Contribution to the following subjects were given: \begin{itemize} \item classification of -actions on manifolds, \item equivariant cohomology and cohomology of reduced spaces, \item fixed points and cohomology, \item Hodge theory, \item moment maps and quantization of manifolds, \item new models for the equivariant cohomology of a space, \item toric varieties. \end{itemize} Especially the informal discussions among participants both with similar and with diverse mathematical background were a very important aspect of the workshop. We believe that the meeting has stimulated further cooperation in the study of actions of Lie groups between mathematicians from different areas.