Some Dynamical and Topological Invariants for symplectic diffeomorphisms
报告人: 夏志宏教授
时间:2023年7月24日15:00-16:00
地点:金沙集团1862cc橙色一楼4106教室
报告摘要:
Consider a symplectic diffeomorphism on a compact symplectic manifold. There are two notable invariants, the flux and rotation vector. We show that the volume flux (a cohomology element) is exactly the Poincare dual of the rotation vector (a homology element). We also establish the relationships between the area flux and the volume flux, and show that the diffeomorphism is Hamiltonian if and only if the rotation vector is zero.
报告人简介:
夏志宏教授,美国西北大学Pancoe讲席教授,大湾区大学(筹)讲席教授,国际知名数学家和天文学家。主要研究动力系统,天体力学,曾解决百年数学难题Painlevé猜测,天体运动的混沌性,Hamilton系统的通有性质和遍历理论中关于拓扑熵的一系列问题。获得多项重大学术奖励,其中包括美国总统青年研究者奖,首批长江学者特聘教授,Sloan Research Fellowship, 首届Blumenthal纯数学进步奖等奖项。2015年创立南方科技大学数学系,以及参与创立未来科学大奖等。