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京东 11.11 红包
Kenji Fukaya(深谷贤治):Virtual Fundamental Chains, J-全纯曲线和Kuranishi Structures
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https://www.youtube.com/watch?v=m4H572CiREc 美国纽约州立大学石溪分校SCGP Name: Kenji Fukaya Title: Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure Date: 2014-01-31 Abstract: The notion of Kuranishi chart and its local construction. In this first talk I focus on the construction of the local Kuranishi chart of the moduli space of pseudo-holomorphic curve. In other words I will explain the construction of local Kuranishi family of the pseudo-holomorphic curves. I first explain the notion of Kuranishi chart. I then review deformation theory of geometric objects and how it is related to the construction of Kuranishi chart. This week I do not yet study compactification of the moduli space so the object I will discuss is a map from nonsingular Riemann surface. 在数学中,尤其是在拓扑学中,Kuranishi structure是scheme structure的smooth analogue。 如果一个拓扑空间被赋予 Kuranishi structure,那么它在局部可以等同于光滑映射的零集,或者这样的零集被有限群的商。 Kuranishi structure是由日本数学家Kenji Fukaya和Kaoru Ono在研究辛几何中的Gromov-Witten不变量和Floer同调时引入的,并以日本数学家Masatake Kuranishi命名。 "Kuranishi spaces" are a class of geometric spaces introduced in 1990 by Fukaya and Ono, as the geometric structure on moduli spaces of J-holomorphic curves in a symplectic manifold, and used in the work of Fukaya, Oh, Ohta and Ono on Lagrangian Floer cohomology and Fukaya categories. Roughly, a Kuranishi space is a topological space X covered by an atlas of 'Kuranishi neighbourhoods' (V, E, Γ,s, ψ), each arising from Kodaira-Spencer-Kuranishi deformations theory. Fukaya–Ono's main goal was to define virtual cycles/chains for these, to be able to define Gromov–Witten invariants, Lagrangian Floer theory, etc. Kenji Fukaya , Yong-Geun Oh , Hiroshi Ohta , Kaoru Ono——《Kuranishi Structures and Virtual Fundamental Chains》:https://doi.org/10.1007/978-981-15-5562-6 Dusa McDuff——《Notes on Kuranishi Atlases》:https://doi.org/10.48550/arXiv.1411.4306 Dusa McDuff, Katrin Wehrheim——《The topology of Kuranishi atlases》:https://doi.org/10.48550/arXiv.1508.01844
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张旭老师的微积分
Kenji Fukaya(深谷贤治):在J-holomorphic curves模空间上Packaging Kuranishi structure的构造
Kenji Fukaya(深谷贤治):Equivariant Kuranishi Structures&Virtual Fundamental Chains
Kenji Fukaya(深谷贤治):J-holomorphic curve with Bubbles的Gluing Analysis和指数衰减估计
Kenji Fukaya(深谷贤治):Wall-crossing and mirror symmetry
Vivek Shende:Axiomatics of the wrapped Fukaya category
Kenji Fukaya(深谷贤治):Equivariant Floer同调
Felix Schlenk:辛嵌入的刚性的多种形式(Symplectic Embeddings)
Yoel Groman:semi-toric SYZ fibrations的Wrapped Fukaya category
Ko Honda:The Giroux Correspondence in Arbitrary Dimensions
Sobhan Seyfaddini:Barcodes and C0 symplectic topology
【IHES】Tom Bridgeland:Geometry from Donaldson-Thomas Invariants
Vincent Humilière:A higher dimensional generalization of the Birkhoff attractor
Ciprian Manolescu:Khovanov Homology and Skein Lasagna Modules
Kenji Fukaya:Floer homologies, Lagrangian correspondence and Atiyah-Floer猜想
Kenji Fukaya(深谷贤治):divisor complement的拉格朗日Floer理论和规范理论
Jo Nelson&Morgan Weiler:ECH of prequantization bundles and lens spaces
Cheuk Yu Mak:Symplectic annular Khovanov homology
Umut Varolgunes:Mirror symmetry via Floer theoretic invariants
Yakov Eliashberg:Weinstein manifolds as cotangent bundles of arboreal spaces
Radmila Sazdanović:Khovanov Homology and Categorifcation 01
Mohammed Abouzaid:Arnold Conjecture and Morava K-theory
Cheuk Yu Mak:Fukaya-Seidel category, Hilbert scheme and category O
Nicole Magill:辛嵌入与Infinite Staircases
Jake Solomon:Degenerate special Lagrangian equation与Lagrangians with boundary
Yakov Eliashberg:How far symplectic flexibility may go
Simon Allais:Contact orderability and spectral selectors
Kenji Fukaya(深谷贤治):arbitrary genus的拉格朗日Floer理论
Austin Christian:Gluing a Morse flow line to itself——II
Ispita Datta:Gluing a Morse flow line to itself——III
Dusa McDuff:将椭球体嵌入Hirzebruch曲面-Symplectic embeddings of 4-dimensional ellipsoids
Ana Rita Pires:辛嵌入问题中的Infinite staircases——2017
Tomasz Mrowka:Floer homology——1.2
Lev Buhovsky:Flexibility in C^0 symplectic geometry
Egor V. Shelukhin:Lagrangian configurations和Hamiltonian maps
【SSOD】Sobhan Seyfaddini:Area-preserving同胚群的代数结构(the simplicity conjecture)——2
【CIRM】Sobhan Seyfaddini:Area-preserving同胚群的代数结构(the simplicity conjecture)
Claude Viterbo:Symplectic Homogenization
Yakov Eliashberg:The program of arborealization