Homotopical Coalgebras, Algebraic Models, and Realizing Derived Equivalences
同伦余代数、代数模型和实现导出等价
基本信息
- 批准号:1811278
- 负责人:
- 金额:$ 24.17万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-06-01 至 2022-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The research projects involve the interplay between the study of algebraic structures and topology, the study of shapes or spaces. Algebraic topologists use algebraic structures to describe and simplify topological phenomena. Spectra, which represent cohomology theories, are algebraic structures built out of topological spaces and hence are useful for translating from one field to the other. In one project, with co-authors, the PI will develop algebraic models for several different topological settings in spectra. The PI continues to train graduate students and disseminate research results. In addition, the PI is involved with several organizations that promote the participation of women and underrepresented minorities in mathematics and science. In the first broad project the PI will continue her work with various coauthors on developing homotopical settings for comodules and coalgebras. The motivations for this project include applications to algebraic K-theory, connections with chromatic homotopy theory and string theory, and development of computational tools. In a second broad project, the PI continues to study when derived equivalences can be realized by underlying richly structured equivalences. This includes recognizing some homotopy categories as rigid, or having a unique (up to equivalence) underlying homotopy theory (as has been shown, for example, for rational circle-equivariant homotopy theory) and also recognizing some homotopy categories as being modeled by non-equivalent homotopy theories.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.
研究项目涉及代数结构和拓扑研究之间的相互作用,形状或空间的研究。代数拓扑学家用代数结构来描述和简化拓扑现象。光谱代表上同调理论,是建立在拓扑空间上的代数结构,因此对于从一个场转换到另一个场是有用的。在一个项目中,PI将与合作者一起开发光谱中几种不同拓扑设置的代数模型。PI继续培养研究生和传播研究成果。此外,PI还参与了几个促进妇女和代表性不足的少数民族参与数学和科学的组织。在第一个广泛的项目中,PI将继续她的工作,与其他合作者一起开发模和余代数的同调设置。该项目的动机包括代数k理论的应用,与色同伦理论和弦理论的联系,以及计算工具的发展。在第二个广泛的项目中,PI继续研究何时可以通过底层结构丰富的等价来实现派生等价。这包括承认一些同伦范畴是刚性的,或者有一个唯一的(直到等价的)底层同伦理论(例如,对于有理圆等变同伦理论),也承认一些同伦范畴是由非等价同伦理论建模的。该奖项反映了美国国家科学基金会的法定使命,并通过使用基金会的知识价值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)
Invariance properties of coHochschild homology
coHochschild 同调的不变性
- DOI:10.1016/j.jpaa.2020.106505
- 发表时间:2021
- 期刊:
- 影响因子:0.8
- 作者:Hess, Kathryn;Shipley, Brooke
- 通讯作者:Shipley, Brooke
Coalgebras in symmetric monoidal categories of spectra
谱对称幺半群中的代数
- DOI:10.4310/hha.2019.v21.n1.a1
- 发表时间:2019
- 期刊:
- 影响因子:0
- 作者:Péroux, Maximilien;Shipley, Brooke
- 通讯作者:Shipley, Brooke
Topological coHochschild homology and the homology of free loop spaces
拓扑coHochschild同调与自由环空间同调
- DOI:10.1007/s00209-021-02879-4
- 发表时间:2022
- 期刊:
- 影响因子:0.8
- 作者:Bohmann, Anna Marie;Gerhardt, Teena;Shipley, Brooke
- 通讯作者:Shipley, Brooke
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Brooke Shipley其他文献
Brooke Shipley的其他文献
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{{ truncateString('Brooke Shipley', 18)}}的其他基金
International Conference on Equivariant Topology and Derived Algebra
等变拓扑与派生代数国际会议
- 批准号:
1901120 - 财政年份:2019
- 资助金额:
$ 24.17万 - 项目类别:
Standard Grant
HOMOTOPICAL ALGEBRA: COALGEBRAS, DGAS, AND RATIONAL EQUIVARIANT SPECTRA
同伦代数:余代数、DGAS 和有理等变谱
- 批准号:
1406468 - 财政年份:2014
- 资助金额:
$ 24.17万 - 项目类别:
Standard Grant
ALGEBRAIC MODELS OF HOMOTOPY THEORIES AND HOMOTOPICAL MODELS OF ALGEBRA
同伦理论的代数模型和代数的同伦模型
- 批准号:
1104396 - 财政年份:2011
- 资助金额:
$ 24.17万 - 项目类别:
Standard Grant
Homotopical Group Theory and Topological Algebraic Geometry, June 2008
同伦群论和拓扑代数几何,2008 年 6 月
- 批准号:
0802491 - 财政年份:2008
- 资助金额:
$ 24.17万 - 项目类别:
Standard Grant
Ring Spectra, DGAs and Derived Equivalences
环谱、DGA 和导出的等价物
- 批准号:
0706877 - 财政年份:2007
- 资助金额:
$ 24.17万 - 项目类别:
Continuing Grant
CAREER: Realizing Derived Equivalences
职业:实现派生等价
- 批准号:
0417206 - 财政年份:2003
- 资助金额:
$ 24.17万 - 项目类别:
Continuing Grant
CAREER: Realizing Derived Equivalences
职业:实现派生等价
- 批准号:
0134938 - 财政年份:2002
- 资助金额:
$ 24.17万 - 项目类别:
Continuing Grant
Mathematical Sciences Postdoctoral Research Fellowships
数学科学博士后研究奖学金
- 批准号:
9508952 - 财政年份:1995
- 资助金额:
$ 24.17万 - 项目类别:
Fellowship Award
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