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学的研究之间的相互作用,形状或空间的研究。代数拓扑学家使用代数结构来描述和简化拓扑现象。 谱,代表上同调理论,是建立在拓扑空间之外的代数结构,因此对于从一个领域到另一个领域的转换是有用的。在一个项目中,与合作者,PI将开发光谱中几种不同拓扑设置的代数模型。PI继续培训研究生并传播研究成果。 此外,PI还参与了几个促进妇女和代表人数不足的少数群体参与数学和科学的组织。在第一个广泛的项目中,PI将继续与各种合著者合作,为余模和余代数开发同伦设置。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开发。在第二个广泛的项目中,PI继续研究何时可以通过基础的丰富结构的等价物来实现衍生等价物。这包括将某些同伦范畴识别为刚性的,或者具有唯一的(直到等价)基本同伦理论(如已经示出的,例如,对于有理圆等变同伦理论),也认识到一些同伦范畴是由非-该奖项反映了NSF的法定使命,并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准。
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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