V
主页
Mark Gross:Introduction to mirror symmetry(The Gross–Siebert program)
发布人
https://www.youtube.com/watch?v=w2WnQSey9xY Mark Gross(生于1965年11月30日)是一位著名的美国数学家,专攻微分几何、代数几何和镜像对称。Mark Gross于1982年在美国康奈尔大学学习,1984年获得学士学位,并于1990年获得美国加州大学伯克利分校的博士学位,在Robin Hartshorne的指导下进行研究,论文主题为《Surfaces in the Four-Dimensional Grassmannian》。从1990年到1993年,他在密歇根大学担任助理教授,并在1992-1993学年休假,在加州大学伯克利分校的SLMath (MSRI) 担任博士后研究员。 他于1993年至1997年在康奈尔大学担任助理教授,并于1997年至2001年担任副教授,然后于2001年至2013年在加州大学圣地亚哥分校担任正教授。2002-2003学年,他是英国华威大学的客座教授。2013年起任英国剑桥大学教授,2016年起任英国剑桥大学国王学院的成员。Mark Gross致力于复几何、代数几何和镜像对称。Mark Gross和Bernd Siebert共同开发了一个纲领(称为Gross–Siebert Program),用于研究代数几何中的镜像对称性。 The Gross–Siebert program建立在Strominger、Yau和Zaslow较早的微分几何提议的基础上,其中the Calabi–Yau manifold is fibred by special Lagrangian tori, and the mirror by dual tori。该纲领的中心思想是将其转化为适当限制的代数几何结构(an algebro-geometric construction in an appropriate limit),涉及与a degenerating family of Calabi–Yau manifolds相关的组合数据。它借鉴了几何学、分析学和组合学的许多领域,对Tropical geometry和non-archimedean geometry、logarithmic geometry、Gromov–Witten invariants的计算、the theory of cluster algebras和combinatorial representation theory等领域产生了深远的影响。 ICM2014 Mark Gross&Bernd Siebert——《Local mirror symmetry in the tropics》: https://doi.org/10.48550/arXiv.1404.3585 ICM2014 Mark Gross&Bernd Siebert——Local mirror symmetry in the tropics:BV1U24y1P77r Mark Gross Homepage:https://www.dpmms.cam.ac.uk/~mg475/ Mark Gross——《Applications of Mirror Symmetry》:https://www.dpmms.cam.ac.uk/~mg475/riverside.pdf Mark Gross——《Mirror symmetry》:https://www.dpmms.cam.ac.uk/~mg475/utah.pdf Mark Gross——《Mirror symmetry and the SYZ conjecture》:https://www.dpmms.cam.ac.uk/~mg475/current.pdf Mark Gross——《Cluster algebras and mirror symmetry》:https://www.dpmms.cam.ac.uk/~mg475/clusters.pdf Mark Gross——《Mirror symmetry and tropical geometry》:https://www.dpmms.cam.ac.uk/~mg475/melbourne.pdf
打开封面
下载高清视频
观看高清视频
视频下载器
Mark Gross:Intrinsic mirror symmetry(The Gross–Siebert program)
【Fields Institute】Mohammed Abouzaid:Bordism of derived orbifolds——3
Bernd Siebert:Canonical wall structure(The Gross–Siebert program)
Shira Tanny:Closing Lemmas and Pseudoholomorphic Curves
【Fields Institute】Mohammed Abouzaid:Bordism of manifolds——1
Misha Bialy:Integrable billiards and rigidity——I
Catherine Cannizzo:Global Homological Mirror Symmetry for Theta Divisors
Ko Honda:The Giroux Correspondence in Arbitrary Dimensions
Mark Gross:Canonical scattering diagrams(The Gross–Siebert program)
Kenji Fukaya(深谷贤治):Wall-crossing and mirror symmetry
Shira Tanny:From Gromov–Witten Theory to the Closing Lemma
Yoel Groman:Toric Calabi-Yau流形的Wrapped Floer theory和Homological mirror symmetry
Tony Yue Yu:Mirror structure constants via non-archimedean analytic disks
Umut Varolgunes:Mirror symmetry via Floer theoretic invariants
Kenji Fukaya(深谷贤治):Zero-dimensional family Floer homology
【Clay Institute】John Pardon:Derived moduli spaces of pseudo-holomorphic curves
Kenji Fukaya(深谷贤治):J-holomorphic curve with Bubbles的Gluing Analysis和指数衰减估计
Mohammed Abouzaid:Complex cobordism and Hamiltonian fibrations
Sobhan Seyfaddini:Barcodes and C0 symplectic topology
Mohammed Abouzaid:Arnold Conjecture and Morava K-theory
Misha Bialy:Integrable billiards and rigidity——II
Yuan Gao:The symplectic formal neighborhood
Vincent Humilière:A higher dimensional generalization of the Birkhoff attractor
Sheel Ganatra(Hiroshi Iritani):Gamma&SYZ conjectures:对Periods的tropical approach
Justin Hilburn:3D Mirror Symmetry的数学理论(symplectic duality)
Yakov Eliashberg:Weinstein manifolds as cotangent bundles of arboreal spaces
Felix Schlenk:辛嵌入的刚性的多种形式(Symplectic Embeddings)
Vivek Shende:Axiomatics of the wrapped Fukaya category
Tobias Ekholm:Large N duality, SFT stretching, and the skein relation
Yakov Eliashberg:How far symplectic flexibility may go
Kenji Fukaya(深谷贤治):Novikov环上的同调镜像对称(Homological Mirror symmetry)
Nick Sheridan(Hiroshi Iritani):The Gamma and SYZ conjectures
Cheuk Yu Mak:Fukaya-Seidel category, Hilbert scheme and category O
Paul Seidel:Calabi-Yau超曲面的Fukaya范畴
Dusa McDuff:将椭球体嵌入Hirzebruch曲面-Symplectic embeddings of 4-dimensional ellipsoids
Ron Donagi:On Integrable Systems and 3D Mirror Symmetry(Deligne-Simpson Problem)
Yoel Groman:semi-toric SYZ fibrations的Wrapped Fukaya category
Eckhard Meinrenken:带边曲面的Teichmüller空间的辛几何——2
Yakov Eliashberg:The program of arborealization
Jake Rasmussen:Introduction to Knot Theory——2.1