中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人： 陈旭佳 博士 （哈佛大学）
题  目：Open Gromov-Witten theory and bounding chains
时  间：2023.09.11（星期一），09:00-10:00
地  点：Zoom会议：857 9156 8842   密码：0911
摘  要：Gromov-Witten invariants count “closed” J-holomorphic curves—closed surfaces, e.g. spheres, tori. Open Gromov-Witten invariants, on the other hand, count “open” J-holomorphic curves---surfaces with boundary, e.g., disks, annuli. Unlike their “closed” counterpart, open Gromov-Witten invariants are often not well-defined. One beautiful way of defining them, due to Fukaya-Oh-Ohta-Ono, is “bounding chains”. I will give an introduction to open Gromov-Witten invariants, bounding chains, and my work that says two seemingly-unrelated definition of open Fromov-Witten invariants are actually the same when they are both defined.

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报告人： 陈旭佳 博士 （哈佛大学）
题  目：Kontsevich’s invariants as topological invariants of configuration space bundles
时  间：2023.09.13（星期三），09:00-10:00
地  点：Zoom会议：837 7933 5082   密码：0913
摘  要：Kontsevich's invariants (also called “configuration space integrals”) are invariants of certain framed smooth manifolds/fiber bundles. The result of Watanabe(’18) showed that Kontsevich’s invariants can distinguish smooth fiber bundles that are isomorphic as topological fiber bundles. I will first give an introduction to Kontsevich's invariants, and then state my work which provides a perspective on how to understand their ability of detecting exotic smooth structures: real blow up operations essentially depends on the smooth structure, and thus given a space/bundle X, the topological invariants of some spaces/bundles obtained by doing some real blow-ups on X can be different for different smooth structures on X.