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pop@ams.org |
Symplectic Topology and Measure-Preserving Dynamical Systems Sunday, July 1– Thursday, July 5 Organizing Committee The algebraic structure of the homeomorphism or diffeomorphisms groups of a manifold and some of their subgroups (volume preserving, symplectic, measure preserving and etc...) has been studied extensively by many mathematicians among them: Anderson, Banyaga, Epstein, Fathi, Herman, Mather, Thurston, Visetti and more recently Entov, Ghys, Gambaudo, Oh, Polterovitch and Py. There is one domain which has remained unknown yet: this is the case of measure preserving homeomorphisms in two dimension. This is the dimension where the symplectic and volume preserving diffeomorphisms coincide. Various recent advances have hinted that the symplectic aspect of the area preserving dynamics provides a serious obstruction to understanding the homeomorphism case in two dimension. Recently, as a byproduct of his study on Floer homology in symplectic geometry, Oh discovered a symplectically defined subgroup of the full measure-preserving homeomorphisms group, the Hamiltonian homeomorphism group, which is a good topological analog to the Hamiltonian diffeomorphism group. Many fundamental questions concerning structure of the Hamiltonian homeomorphism group itself remain open. And in two dimension it also sheds some light on the algebraic properties of the measure preserving homeomorphism group itself. An important uniqueness theorem on the topological Hamiltonians, which are associated to each continuous flow on this group, has been proved by Viterbo and Oh. This provides the ground for the Hamiltonian topological dynamics, which is expected to generalize two dimensional area preserving dynamics in high dimensions in a nontrivial way. The subject of the proposed workshop is at the intersection of low dimensional topology, low-dimensional dynamical systems and C^0-symplectic topology. The purpose of the workshop is to bring in specialists from different fields of mathematics to exchange knowledge and techniques to attack some of these problems, and to introduce young researchers to a topic that anticipates much development in the near future. The workshop will have two to three mini-courses including at least one on symplectic methods in Hamiltonian dynamics and one on low dimensional dynamics. A conference webpage is maintained at http://math.wisc.edu/~oh/src07.html. |
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