FRG: Collaborative Research in Gauge Theory
FRG:规范理论的合作研究
基本信息
- 批准号:1952755
- 负责人:
- 金额:$ 31.29万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2020
- 资助国家:美国
- 起止时间:2020-06-01 至 2024-11-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Understanding of the structure of the four-dimensional universe in which we live is a key topic of investigation in modern mathematics and physics. Gauge theory is a crucial tool for the study of the mathematical structures that provide the context for standard models of the physical world. The research supported by this project will develop new mathematical tools and theories that will help test such models and advance our understanding of four-dimensional spaces. A key mathematical idea is the interaction between three-dimensional theories known as Floer theories and the study of invariants of four-dimensional spaces. In addition the project provides research training opportunities for graduate students.This project will develop and extend invariants including abelian gauge theoretic models, cobordism invariants arising from the critical values of Morse like functions such as Daemi's Gamma invariant, equivariant extensions such as equivariant singular instanton knot homology, and new parameterized invariants that combine Konno adjunction-style complexes with homotopy invariants of families. It will also translate structures uncovered in some gauge theory packages to other packages, for example translating L-space notions from Heegaard Floer theory to analogues in the instanton case, or equivariant structures from the Seiberg-Witten Floer theory to the Heegaard Floer theory. Topological applications will include new insights into knot concordance, homology cobordism, diffeomorphism groups of 4-manifolds, and SU(2) representations of 3-manifold groups.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
理解我们所生活的四维宇宙的结构是现代数学和物理学研究的一个关键课题。规范理论是研究数学结构的重要工具,这些结构为物理世界的标准模型提供了背景。该项目支持的研究将开发新的数学工具和理论,有助于测试这种模型,并促进我们对四维空间的理解。一个关键的数学思想是被称为弗洛尔理论的三维理论和四维空间不变量研究之间的相互作用。此外,该项目还将为研究生提供研究培训机会。本项目将开发和扩展不变量,包括阿贝尔规范理论模型,由类Morse函数临界值产生的协边不变量,如Daemi的Gamma不变量,等变扩展,如等变奇异瞬子结同调,以及将Konno附加型复形与族的同伦不变量相结合的新的参数化不变量。它还将把一些规范理论包中未涉及的结构翻译到其他包中,例如将L空间概念从Heegaard Floer理论翻译成瞬子情况下的类比,或者将Seiberg-Witten Floer理论的同变结构翻译成Heegaard Floer理论。拓扑学应用将包括对纽结调和、同调共边、4-流形的微分同胚群和3-流形群的SU(2)表示的新见解。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On non‐orientable surfaces embedded in 4‐manifolds
在嵌入 4 流形的不可定向表面上
- DOI:10.1112/topo.12188
- 发表时间:2021
- 期刊:
- 影响因子:1.1
- 作者:Auckly, David;Sadykov, Rustam
- 通讯作者:Sadykov, Rustam
Equivariant hyperbolization of 3-manifolds via homology cobordisms
- DOI:10.1016/j.topol.2023.108485
- 发表时间:2018-04
- 期刊:
- 影响因子:0.6
- 作者:D. Auckly;H. Kim;P. Melvin;Daniel Ruberman
- 通讯作者:D. Auckly;H. Kim;P. Melvin;Daniel Ruberman
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David Auckly其他文献
David Auckly的其他文献
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{{ truncateString('David Auckly', 18)}}的其他基金
Collaborative Research: Conference: 2023-2025 Kansas Mathematics Graduate Student Conference
合作研究:会议:2023-2025年堪萨斯数学研究生会议
- 批准号:
2326561 - 财政年份:2023
- 资助金额:
$ 31.29万 - 项目类别:
Standard Grant
Midwest Geometry Conference 2019-2021
中西部几何会议 2019-2021
- 批准号:
1855861 - 财政年份:2019
- 资助金额:
$ 31.29万 - 项目类别:
Standard Grant
NSF INCLUDES DDLP: Indigenous Math Circles Communities
NSF 包括 DDLP:本土数学圈社区
- 批准号:
1744474 - 财政年份:2017
- 资助金额:
$ 31.29万 - 项目类别:
Standard Grant
The Geometry and Topology of Quantum Invariants of Knots and 3-Manifolds
结和3-流形的量子不变量的几何和拓扑
- 批准号:
0604994 - 财政年份:2006
- 资助金额:
$ 31.29万 - 项目类别:
Standard Grant
Brainstorming and Barnstorming: An REU site at KSU
头脑风暴和巡回演讲:KSU 的 REU 站点
- 批准号:
0453572 - 财政年份:2005
- 资助金额:
$ 31.29万 - 项目类别:
Continuing Grant
Mathematical Sciences: Postdoctoral Research Fellowship
数学科学:博士后研究奖学金
- 批准号:
9407465 - 财政年份:1994
- 资助金额:
$ 31.29万 - 项目类别:
Fellowship Award
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