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Leonid Polterovich
Visit: February 22 - 27, 2010
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Series Title:
"Function theory on symplectic manifolds"
Lectures:
2/23 Tuesday @ 2:00 - 3:00 pm in MS 6627
2/24 Wednesday @ 2:00 - 3:00 pm in MS 6627
2/25 Thursday @ 2:00 - 3:00 pm in MS 6221
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Lecture 1
Symplectic rigidity and quantum-classical correspondence
Tuesday, Feb. 23, 2010 2:00 PM, MS 6627
Lecture 2
Geometry and analysis of Poisson brackets
Wednesday, Feb. 24, 2010 2:00 PM, MS 6627
Lecture 3
Applications of function theory to symplectic topology and Hamiltonian dynamics
Thursday, Feb. 25, 2010 2:00 PM, MS 6221
ABSTRACT
Symplectic geometry and topology is a rapidly developing field of mathematics which originally appeared as a geometric tool for problems of classical mechanics. The “symplectic revolution” of the 1980s gave rise to the discovery of surprising rigidity phenomena involving symplectic manifolds, their subsets and diffeomorphisms. A number of recent advances show that there is yet another manifestation of symplectic rigidity, taking place in function spaces associated to a symplectic manifold. These spaces exhibit unexpected properties and interesting structures, giving rise to an alternative intuition and new tools in symplectic topology. I shall discuss these developments as well as links to other subjects such as group theory, Lie algebras and foundations of quantum mechanics. The colloquium-type lectures are based on a series of joint works with Michael Entov.
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