Northeast Conferences on Geometry and Topology of 4-Manifolds
东北四流形几何与拓扑会议
基本信息
- 批准号:1522633
- 负责人:
- 金额:$ 4.97万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2015
- 资助国家:美国
- 起止时间:2015-04-01 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The "Northeast Conferences on Geometry and Topology of 4-manifolds" series will have two meetings in 2015-2016, both at the University of Massachusetts, Amherst. The first conference, entitled "Geometry and Topology of Symplectic 4-Manifolds," will meet between April 24-26, 2015, and the second, entitled "Floer Homologies, Gauge Theory, and Topology of 4-Manifolds," will meet in fall 2016. The conference series focuses on the geometry and topology of 4-manifolds, regarded as a melting pot for various research areas, such as low dimensional topology, contact, symplectic, complex and differential geometry, geometric analysis, and mathematical physics. The organizers plan to bring together leading experts and rising young researchers from across the country as speakers for each meeting and to support participation of interested researchers and graduate students, especially from the institutions in the Northeast. An objective of the conference series is to fertilize new research directions by increasing interaction and collaboration among the wealth of geometers and topologists in Massachusetts, New York, New Jersey and Connecticut, particularly among graduate students, junior researchers, and their more senior colleagues, while providing all with a panorama of the subject area through a variety of talks and discussion sessions. The series will help build a regional network and support ties among graduate students, faculty, and other researchers throughout the Northeast.The themes for both conferences are chosen from the most active and dynamic fields in recent years. Taubes' work connecting Seiberg-Witten gauge theory and symplectic topology has had great impact on both symplectic geometry and 4-dimensional smooth topology, while work of Donaldson and Gompf has led to many new constructions and applications of Lefschetz fibrations. The advances led to deep understanding of the internal structure of symplectic 4-manifolds. Remarkably, this led to the complete smooth and symplectic classification of symplectic 4-manifolds of negative Kodaira dimension. These will be the main topics of the first conference. On the other hand, gauge theory has had an enormous impact on the study of smooth 4-manifolds, starting with the seminal work of Donaldson in the 1980's and the introduction of Seiberg-Witten theory some 10 years later. Coupled with new methods for building 4-manifolds, this has led to the constructions of exotic smooth manifolds in many homotopy types, and to an understanding of the internal structure of smooth 4-manifolds. The deepest results of recent years have been based on the use of gauge theoretic invariants of 3-manifolds known as Floer homology theories, which give rise in turn to invariants of 4-manifolds with boundary. The second conference will focus on these invariants for all smooth 4-manifolds.Web link for the Spring 2015 conference: http://people.math.umass.edu/~baykur/Symplectic4manifoldsConference.html
“东北4流形几何与拓扑会议”系列将于2015-2016年在马萨诸塞大学阿姆赫斯特分校举行两次会议。第一届会议的主题是“辛4流形的几何和拓扑”,将于2015年4月24日至26日举行,第二届会议的主题是“花同调、规范理论和4流形的拓扑”,将于2016年秋季举行。该系列会议的重点是4流形的几何和拓扑,被视为各种研究领域的大熔炉,如低维拓扑,接触,辛,复杂和微分几何,几何分析和数学物理。组织者计划召集来自全国各地的顶尖专家和崭露头角的年轻研究人员作为每次会议的演讲者,并支持感兴趣的研究人员和研究生的参与,特别是来自东北院校的研究人员。会议系列的一个目标是通过增加马萨诸塞、纽约、新泽西和康涅狄格的几何学家和拓扑学家之间的互动和合作,特别是研究生、初级研究人员和他们的高级同事之间的互动和合作,来丰富新的研究方向,同时通过各种讲座和讨论会议为所有人提供主题领域的全景。该系列将有助于建立一个区域网络,并支持研究生,教师和其他研究人员在整个东北之间的联系。这两次会议的主题都选自近年来最活跃和最具活力的领域。Taubes将Seiberg-Witten规范理论与辛拓扑联系起来的工作对辛几何和四维光滑拓扑都产生了重大影响,而Donaldson和Gompf的工作则导致了许多新的Lefschetz颤振的构造和应用。这些进展使人们对辛4流形的内部结构有了更深刻的认识。值得注意的是,这导致了负Kodaira维辛4流形的完全光滑和辛分类。这些将是第一次会议的主要议题。另一方面,规范理论对光滑4流形的研究产生了巨大的影响,从20世纪80年代Donaldson的开创性工作开始,到大约10年后Seiberg-Witten理论的引入。结合构造4流形的新方法,这导致了许多同伦类型的奇异光滑流形的构造,并对光滑4流形的内部结构有了了解。近年来最深刻的结果是基于3-流形的规范论不变量的使用,即花同调理论,它反过来又产生了具有边界的4-流形的不变量。第二次会议将集中讨论所有光滑4流形的不变量。2015年春季会议的网站链接:http://people.math.umass.edu/~baykur/Symplectic4manifoldsConference.html
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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R. Inanc Baykur其他文献
Positive factorizations of mapping classes
映射类的正分解
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0.7
- 作者:
R. Inanc Baykur;N. Monden and J. Van Horn-Morris - 通讯作者:
N. Monden and J. Van Horn-Morris
Constructing Lefschetz brations via daisy substitutions
通过雏菊替换构造 Lefschetz brations
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0.6
- 作者:
R. Inanc Baykur;N. Monden and J. Van Horn-Morris;N. Monden and K. Yoshihara;Anar Akhmedov and Naoyuki Monden - 通讯作者:
Anar Akhmedov and Naoyuki Monden
「相対性理論とベクトル解析」
《相对论与矢量分析》
- DOI:
- 发表时间:
2014 - 期刊:
- 影响因子:0
- 作者:
R. Inanc Baykur;Seiichi Kamada;Hideo Kojima;山田澄生 - 通讯作者:
山田澄生
On stable commutator lengths of Dehn twists along separating curves
沿分离曲线 Dehn 扭曲的稳定换向器长度
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0.5
- 作者:
R. Inanc Baykur;N. Monden and J. Van Horn-Morris;N. Monden and K. Yoshihara - 通讯作者:
N. Monden and K. Yoshihara
R. Inanc Baykur的其他文献
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{{ truncateString('R. Inanc Baykur', 18)}}的其他基金
Topology of smooth and symplectic 4-manifolds
光滑和辛4流形的拓扑
- 批准号:
1510395 - 财政年份:2015
- 资助金额:
$ 4.97万 - 项目类别:
Standard Grant
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