Coisotropic Submanifolds of Symplectic Manifolds and Leafwise Fixed Points
主 题: Coisotropic Submanifolds of Symplectic Manifolds and Leafwise Fixed Points
报告人: Fabian Ziltener
时 间: 2017-02-23 14:00 - 2017-02-23 15:00
地 点: Room 77201，Jingchunyuan 78,BICMR
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\n\tAbstract: \n<\/p>\n
\n\tConsider a symplectic manifold\n$(M,\\omega)$, a closed coisotropic submanifold $N$ of $M$, and a Hamiltonian\ndiffeomorphism $\\phi$ on $M$. A leafwise fixed point for $\\phi$ is a point\n$x\\in N$ that under $\\phi$ is mapped to its isotropic leaf. These points generalize\nfixed points and Lagrangian intersection points. In classical mechanics\nleafwise fixed points correspond to trajectories that are changed only by a\ntime-shift, when an autonomous mechanical system is perturbed in a\ntime-dependent way.
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\n\tJ. Moser posed the following problem: Find conditions under which\nleafwise fixed points exist and provide a lower bound on their number. A\nspecial case of this problem is V.I. Arnold\'s conjecture about fixed points of\nHamiltonian diffeomorphisms.
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\n\tIn this talk the speaker will\nprovide solutions to Moser\'s problem. As an application, the sphere is not\nsymplectically squeezable. This improves M. Gromov\'s symplectic nonsqueezing\nresult.
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