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京东 11.11 红包
Michael Hutchings:Braid Stability for Periodic Orbits of Area-preserving曲面微分同胚
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https://www.youtube.com/watch?v=pPUNzXhzJ8Y Institute for Advanced Study Joint IAS/Princeton University Symplectic Geometry Seminar Seminar site:http://www.math.tau.ac.il/~sarabt/zoominar/ Topic: Braid Stability for Periodic Orbits of Area-preserving Surface Diffeomorphisms Speaker: Michael Hutchings Affiliation: University of California, Berkeley Date: April 03, 2023 Michael Hutchings是一位著名的美国数学家,现任美国加州大学伯克利分校数学教授(University of California, Berkeley),主要研究低维拓扑、辛拓扑和辛几何。他以证明the double bubble conjecture on the shape of two-chambered soap bubbles,以及他在circle-valued Morse theory和定义embedded contact homology/ECH的工作而闻名。他于1998年博士毕业于美国哈佛大学(Harvard University),导师为美国著名数学家Clifford Henry Taubes。在斯坦福大学、德国波恩马克斯·普朗克数学研究所和美国普林斯顿高等研究院/IAS担任博士后和访问职位后,他于2001年加入加州大学伯克利分校。他于2003年获得Sloan Research Fellowship。他是2010年国际数学家大会/ICM的45分钟报告人。报告内容是《Embedded contact homology and its applications》。2012年,他成为美国数学学会会员。 他在circle-valued Morse theory方面的工作(部分与Yi-Jen Lee合作)研究了由circle-valued Morse theory产生的torsion invariants,更一般地说,是closed 1-forms,并将它们与三维Seiberg–Witten invariants和Meng–Taubes theorem联系起来,类似于四维的Taubes' Gromov–Seiberg–Witten theorem。 他的工作主体涉及embedded contact homology/ECH。ECH是三维流形的Seiberg-Witten-Floer同调的全纯曲线模型,因此是某些带边四维流形的Taubes's Gromov invariant的一个版本。与ECH相关的思想在Taubes证明三维流形的Weinstein conjecture中很重要。Embedded contact homology现在已经被证明与monopole Floer homology (Kutluhan–Lee–Taubes)和Heegaard Floer homology (Colin–Ghiggini–Honda)同构。Hutchings还引入了一系列称为ECH capacities的symplectic capacities,它可用于Liouville domains的embedding problems。 Michael Hutchings homepage:https://math.berkeley.edu/~hutching/ M.Hutchings——与Viterbo's conjectures相关的例子:BV1S84y187Sn M.Hutchings——Two or infinitely many Reeb orbits:BV1tc411j7DH M.Hutchings——Overview of ECH and OBG:BV1GY4y1X73D 加州大学伯克利分校/UC Berkeley—数学53—Michael Hutchings—多元微积分:BV1ic411L728
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