V
主页
京东 11.11 红包
David White:Symplectic Instanton Homology of Knots and Links in 3-manifolds
发布人
https://www.youtube.com/watch?v=31jlZKiv-p0 Institute for Advanced Study Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Seminar site:http://www.math.tau.ac.il/~sarabt/zoominar/ Topic: Symplectic Instanton Homology of Knots and Links in 3-manifolds Speaker: David White Affiliation: North Carolina State University Date: February 10, 2023 Powerful homology invariants of knots in 3-manifolds have emerged from both the gauge-theoretic and the symplectic kinds of Floer theory: on the gauge-theoretic side is the instanton knot homology of Kronheimer-Mrowka, and on the symplectic the (Heegaard) knot Floer homology developed independently by Ozsváth-Szabó and by Rasmussen. These theories are conjecturally equivalent, but a precise connection between the gauge-theoretic and symplectic sides here remains to be understood. We describe a construction designed to translate singular instanton knot homology more directly into the symplectic domain, a so-called symplectic instanton knot homology: We define a Lagrangian Floer homology invariant of knots and links which extends a 3-manifold invariant developed by H. Horton. The construction proceeds by using specialized Heegaard diagrams to parametrize an intersection of traceless SU(2) character varieties. The latter is in fact an intersection of Lagrangians in a symplectic manifold, giving rise to a Lagrangian Floer homology. We discuss its relation to singular instanton knot homology, as well as the formal properties which this suggests and methods to prove these properties. David White是美国北卡罗来纳州立大学(北卡罗来纳州)/North Carolina State University (NC State)数学系的五年级博士生。David White的研究领域是低维流形拓扑(low-dimensional manifold topology)和辛几何(symplectic geometry),尤其是Floer理论的应用。 他对开展以下研究特别感兴趣:knots和links的Floer-homological relative invariants的构造,以及Atiyah-Floer猜想的变体。David White的导师是Tye Lidman。David White于2011获得了杜克大学/Duke University的学士学位,主修哲学和数学。 之后,他在2017年返回学术界之前曾担任软件开发人员多年。 David White homepage:https://dave-white.github.io/
打开封面
下载高清视频
观看高清视频
视频下载器
Roman Krutowski:Maslov Index Formula in Heegaard Floer Homology
Radmila Sazdanović:Khovanov Homology and Categorifcation 01
Radmila Sazdanović:Khovanov Homology and Categorifcation 02
Jean Gutt:Equivariant Symplectic Homology
Yakov Eliashberg:How far symplectic flexibility may go
Michael Hutchings:Classification of Some Open Toric Domains
Mohammed Abouzaid:Complex cobordism and Hamiltonian fibrations
【IHES】Tom Bridgeland:Geometry from Donaldson-Thomas Invariants
Cheuk Yu Mak:Symplectic annular Khovanov homology
Claude Viterbo:Symplectic metrics and stochastic Hamiltonian PDE
Marco Mazzucchelli:Spectral characterizations of Besse and Zoll Reeb flows
Pazit Haim-Kislev:Insights and Challenges in Symplectic Capacities
Joé Brendel&Felix Schlenk:关于toric symplectic manifolds中实拉格朗日子流形的拓扑——03
Sobhan Seyfaddini:C^0 Contact Topology and Symplectic Topology
Brayan Ferreira:Gromov Width of Disk Cotangent Bundles of Spheres of Revolution
数学中的重构问题,丹 · 马格利特| 伦敦数学会玛丽·卡特赖特讲座
Ciprian Manolescu:什么是Floer homotopy类型?
Ciprian Manolescu:A knot Floer stable homotopy type
Vincent Humilière:A higher dimensional generalization of the Birkhoff attractor
【Fields Institute】Mohammed Abouzaid:Bordism of orbifolds——2
Yakov Eliashberg:Weinstein manifolds as cotangent bundles of arboreal spaces
Tobias Ekholm:Skein module curve counts and recursion
Ko Honda:The Giroux Correspondence in Arbitrary Dimensions
Tomasz Mrowka:Floer homology——1.2
Michael Hutchings:Braid Stability for Periodic Orbits of Area-preserving曲面微分同胚
Joé Brendel&Felix Schlenk:关于toric symplectic manifolds中实拉格朗日子流形的拓扑——01
Ciprian Manolescu:Khovanov Homology and Skein Lasagna Modules
【IAS】Leonid Polterovich:Quantum footprints of symplectic rigidity
Joé Brendel&Felix Schlenk:关于toric symplectic manifolds中实拉格朗日子流形的拓扑——02
Claude Viterbo:Symplectic Homogenization
Kenji Fukaya(深谷贤治):J-holomorphic curve with Bubbles的Gluing Analysis和指数衰减估计
Shira Tanny:Closing Lemmas and Pseudoholomorphic Curves
【Fields Institute】Mohammed Abouzaid:Bordism of manifolds——1
Ivan Smith:Lagrangian Whitney sphere links
Yaron Ostrover:两个猜想的故事:从Mahler到Viterbo(Symplectic Measurements)
Peter Kronheimer:空间图的四色定理(Four-Color Theorem)和瞬子不变量(Instanton Invariant)——1
Tomasz Mrowka:Floer homology——4.1
Claude Viterbo:Area preserving maps-the symplectic viewpoint
Sobhan Seyfaddini:C^0 Limits of Hamiltonian Paths and Spectral Invariants
Tobias Ekholm:colored HOMFLY polynomial的高亏格纽结切触同调和recursion