Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties

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. 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:

• classification of $G$-actions on manifolds,
• equivariant cohomology and cohomology of reduced spaces,
• fixed points and cohomology,
• Hodge theory,
• moment maps and quantization of manifolds,
• new models for the equivariant cohomology of a space,
• toric varieties.

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.