CAREER: ARITHMETIC STRUCTURE OF HOMOTOPY THEORY
职业:同伦论的算术结构
基本信息
- 批准号:1050466
- 负责人:
- 金额:$ 43.41万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-07-01 至 2015-03-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The PI will investigate geometric invariants which associate automorphic forms to structured manifolds. The homotopy theoretic construction of these invariants is related to properties of holomorphic Eisenstein series on unitary groups. A geometric construction of these invariants will also be pursued, using higher dimensional field theories. These geometric invariants, when regarded as invariants of framed manifolds, give rise to invariants of elements of the stable homotopy groups of spheres. The arithmetic properties of such families of automorphic forms arising from periodic families in the stable homotopy groups of spheres will also be investigated. Similar analysis for unstable homotopy groups of spheres will be considered using Goodwillie calculus. The PI also proposes an educational program to identify and develop diverse undergraduate talent at MIT through ROUTE partnerships (Reading Outreach for Undergraduate Talent Exploration). These partnerships will pair MIT undergraduates who are interested in the mathematics major, but may not know what mathematicians do, with graduate student mentors to engage in semester long directed reading projects. These mentoring partnerships will be targeted to undergraduates who are members of underrepresented minority groups. The PI will solicit undergraduate research projects from outstanding students completing the ROUTE program, some of which will advance his own research agenda.The proposed research will advance our current understanding of geometry. It will also link this new understanding to physics, as the proposed research involves generalizations of string theory. As the proposed research involves using number theory to study geometry, it will associate new arithmetic structures to known geometric structures. The ROUTE partnerships will create a pathway to tap the diverse talent pool represented by the MIT undergraduate population, and will attract a more diverse collection of individuals to pursue the mathematics major.
PI将研究将自守形式与结构流形相关联的几何不变量。 这些不变量的同伦理论构造与酉群上全纯Eisenstein级数的性质有关。 这些不变量的几何结构也将采用高维场论。 这些几何不变量,当被视为框架流形的不变量时,会产生球面的稳定同伦群的元素的不变量。 我们也将研究这些自守形式族的算术性质,这些自守形式族是由球面的稳定同伦群中的周期族产生的。球的不稳定同伦群的类似分析将考虑使用古德威利演算。 PI还提出了一个教育计划,以确定和发展多样化的本科人才在麻省理工学院通过路由伙伴关系(阅读拓展本科人才探索)。 这些合作伙伴关系将配对麻省理工学院的本科生谁是有兴趣的数学专业,但可能不知道数学家做什么,与研究生导师从事为期一学期的定向阅读项目。这些指导伙伴关系将针对代表性不足的少数群体的本科生。 PI将从完成ROUTE项目的优秀学生中征集本科研究项目,其中一些将推进他自己的研究议程。拟议的研究将推进我们目前对几何的理解。 它还将把这种新的理解与物理学联系起来,因为拟议的研究涉及弦理论的推广。 由于拟议的研究涉及使用数论来研究几何,它将把新的算术结构与已知的几何结构联系起来。 ROUTE合作伙伴关系将创建一个途径,以利用麻省理工学院本科生人口为代表的多元化人才库,并将吸引更多元化的个人来追求数学专业。
项目成果
期刊论文数量(0)
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科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Mark Behrens其他文献
Topological Automorphic Forms
拓扑自守形式
- DOI:
10.1090/s0065-9266-09-00573-0 - 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
Mark Behrens;Tyler Lawson - 通讯作者:
Tyler Lawson
On the top-weight rational cohomology of A g
关于 A g 的顶权有理上同调
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
M. A. B. Randt;J. U. B. Ruce;M. E. C. Han;M. A. M. Elo;G. W. M. Oreland;C. O. W. Olfe;Mladen Bestvina;Mark Gross;Dan Abramovich;Arend Bayer;Mark Behrens;Jim Bryan;Mike Freedman;Colin Rourke;Roman Sauer - 通讯作者:
Roman Sauer
Mark Behrens的其他文献
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{{ truncateString('Mark Behrens', 18)}}的其他基金
Conference: Midwest Topology Seminar
会议:中西部拓扑研讨会
- 批准号:
2341204 - 财政年份:2024
- 资助金额:
$ 43.41万 - 项目类别:
Standard Grant
Equivariant and Motivic Deformations of Stable Homotopy Theory
稳定同伦理论的等变和动机变形
- 批准号:
2005476 - 财政年份:2020
- 资助金额:
$ 43.41万 - 项目类别:
Standard Grant
Chromatic homotopy - stable and unstable
色同伦 - 稳定和不稳定
- 批准号:
1611786 - 财政年份:2016
- 资助金额:
$ 43.41万 - 项目类别:
Continuing Grant
CAREER: ARITHMETIC STRUCTURE OF HOMOTOPY THEORY
职业:同伦论的算术结构
- 批准号:
1452111 - 财政年份:2014
- 资助金额:
$ 43.41万 - 项目类别:
Continuing Grant
Conference Proposal: CURRENT AND CLASSICAL THEMES IN HOMOTOPY THEORY
会议提案:同伦理论的当前和经典主题
- 批准号:
0904858 - 财政年份:2009
- 资助金额:
$ 43.41万 - 项目类别:
Standard Grant
Local and global methods in homotopy theory
同伦理论中的局部和全局方法
- 批准号:
0605100 - 财政年份:2006
- 资助金额:
$ 43.41万 - 项目类别:
Continuing Grant
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