This biweekly online seminar is joint-organized by ShanghaiTech University, USTC-IGP, Yonsei University, and Zhejiang University. This seminar features symplectic and contact geometers presenting current developments on a wide range of topics in these two fields. The talks are aimed at a broad audience. See also our symplectic reading seminar.
Organizing committee: Hansol Hong, Junwu Tu, Weiwei Wu, Jun Zhang.
Title: Complex cobordism, Hamiltonian loops and global Kuranishi chart
Abstract: Consider a smooth submersion from a symplectic manifold P to the complex line with symplectic fibers. Then we prove that the cohomology of P over the integers is additively isomorphic to the cohomology of the fiber times the base. More generally, we prove such an isomorphism holds with respect to any complex oriented cohomology theory, such as complex cobordism. These results are new even in the special case of smooth projective morphisms to the complex line. To prove our result we use Morava K theories. Our proof also contains a new construction of a global Kuranishi chart for the moduli space of curves. We will mainly focus on the construction of global Kuranishi charts. This is joint work with Abouzaid and Smith.
Zoom ID: 841 2143 4035 Password: 462059
Zoom link: https://us06web.zoom.us/j/84121434035?pwd=alVrNDVJc1A1ZS9WV0hKSEpmQlNmUT09
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Time: March 23th, 2023 at 9:30am (Beijing time) Mohan Swaminathan (Stanford University)Title: Global charts and a product formula for symplectic Gromov-Witten invariants
Abstract: I will describe a construction of global Kuranishi charts for the moduli space of stable maps in a closed symplectic manifold (generalizing a construction of Abouzaid-McLean-Smith in genus 0). I will also discuss some applications of this construction including a product formula for Gromov-Witten invariants of symplectic manifolds. This is based on joint work with Amanda Hirschi.
Zoom ID: 876 9005 3829 Password: 512624
Zoom link: https://us06web.zoom.us/j/87690053829?pwd=aHVQRWRBL2ZtSGh1aEhTMUgzVS9xZz09
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WE WILL USE THE FOLLOWING RECURRING MEETING LINK IN THE FUTURE:
Zoom ID: 858 0911 5251 Password: 528485
Zoom link: https://us06web.zoom.us/j/85809115251?pwd=MEQ1RnBoSjRlWjQ1NGlpOFdFb3pQUT09
Title: Higher dimensional Heegaard Floer homology and Hecke algebras
Abstract: Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a special case, it's related to symplectic Khovanov homology. In this talk, we discuss HDHF of cotangent fibers of the cotangent bundle of an oriented surface and show that it is isomorphic to various Hecke algebras. This is a joint work with Ko Honda and Tianyu Yuan.
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Title: Interleaving Distance for Sheaves and Symplectic Geometry
Abstract: The interleaving distance is a canonical pseudo-distance for persistence modules, and its stability property plays an important role in topological data analysis. Recently, it has been generalized to a pseudo-distance on the derived category of sheaves. In this talk, I show that the distance for sheaves has the stability property with respect to Hamiltonian deformation, and it can be used to give a lower bound of displacement energy. I would also like to explain our result on the completeness of the distance and its application to C^0-symplectic geometry. Joint work with Tomohiro Asano.
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Title: A Characterization of Heaviness in terms of Relative Symplectic Cohomology
Entov and Polterovich introduced the notion of heaviness and super-heaviness to characterize some intersection phenomena of compact subsets of a symplectic manifold around 15 years ago. More recently, for a completely different reason, Varolgunes introduced a Floer theory for compact sets called relative symplectic cohomology, which also characterizes certain intersection phenomena. We will try to explain how these are related. Interestingly, we get non-trivial applications in both directions by establishing this relation. This is joint work with Yuhan Sun and Umut Varolgunes.
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