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Host: Centre de recherches mathématiques
Homepage: http://www.crm.umontreal.ca/act/theme/theme_2001-2002_an.html
Email: activites@CRM.UMontreal.CA
Organizers: Niky Kamran (McGill), Boris Khesin (Toronto)
Description:
From a differential-geometric point-of-view, infinite-dimensional Lie groups arise as automorphism groups of various geometric structures on the
manifolds, such as a volume form, a foliation, a contact structure or a symplectic structure. The study of these infinite-dimensional Lie groups
becomes a fundamental problem in areas of mathematics as diverse as hydrodynamics and symplectic topology. Another wide class of
infinite-dimensional Lie groups is formed by loop groups, Kac-Moody groups, and more generally, by gauge groups on manifolds of arbitrary
dimension. The successes in the study of these groups have been immensely fruitful both in low-dimensional geometry and topology and in quantum
field theory. Infinite-dimensional Lie groups are also fundamental in the theory of integrable systems and their hierarchies. In this context, their action
becomes quite explicit on spaces of pseudo-differential and Fourier integral operators.
The purpose of this mini-program will be to review some of the significant recent developments in the above areas and to explore some of the important open problems.
Date received: October 08, 2001
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