Applications of equivariant stable homotopy theory

等变稳定同伦理论的应用

基本信息

  • 批准号:
    2301520
  • 负责人:
  • 金额:
    $ 15.38万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2023
  • 资助国家:
    美国
  • 起止时间:
    2023-08-01 至 2026-07-31
  • 项目状态:
    未结题

项目摘要

Algebraic topology is the study of topological objects, such as topological spaces, through algebraic invariants that do not change when spaces are continuously deformed. Stable homotopy theory, a central part of algebraic topology, expands from the study of spaces to that of spectra, which are "stabilized spaces" that also represent generalized cohomology theories, or ways to assign algebraic invariants to spaces or other spectra. Equivariant stable homotopy theory further adds to spectra the actions of groups, which can be thought of as ways to map a spectrum to itself in composable and invertible ways. Equivariant stable homotopy theory has grown to be an important tool that offers insights into many deep questions in algebraic topology. The techniques of equivariant stable homotopy theory have also found applications in other areas of mathematics, including algebraic geometry and number theory. The broader impact aspect of the project includes mentoring of graduate and undergraduate students in mathematical research. The principal investigator (PI) will also continue outreach efforts by working to make her research area accessible to the public.This project includes a circle of ideas in equivariant stable homotopy theory. The PI will continue her ongoing work on equivariant complex cobordism spectra, in particular the extension of her previous calculation of the coefficients of such spectra for primary p-groups to more general groups. This has important implications to the study of equivariant formal group laws, another part of the project that the PI will pursue. The PI will also investigate applications to her recent calculation, together with her collaborators, of the equivariant Mackey Steenrod algebra for odd primes. Specifically, one such application the PI is pursing is the construction of odd-primary versions of the Real Brow-Peterson spectrum. A closely related question is the construction and understanding of equivariant elliptic and Barsotti-Tate cohomologies, as well as the formal group laws associated with these spectra. The PI will also continue her ongoing project, along with her collaborators, in the calculation of self-conjugate and double-real cobordism spectra.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.
代数拓扑学是通过代数不变量来研究拓扑对象,如拓扑空间,当空间连续变形时,代数不变量不会改变。稳定同伦理论是代数拓扑学的核心部分,它从空间的研究扩展到谱的研究,谱是“稳定空间”,也代表广义上同调理论,或将代数不变量分配给空间或其他谱的方法。等变稳定同伦理论进一步将群的作用添加到谱中,这可以被认为是以可合成和可逆的方式将谱映射到自身的方法。等变稳定同伦理论已经发展成为一个重要的工具,它为代数拓扑学中的许多深层次问题提供了深刻的见解。等变稳定同伦理论的技巧也在数学的其他领域得到应用,包括代数几何和数论。该项目更广泛的影响方面包括指导研究生和本科生的数学研究。首席研究员(PI)也将继续努力,使她的研究领域向公众开放。这个项目包括一个等变稳定同伦理论的思想圈。PI将继续她正在进行的等变复配边光谱的工作,特别是她以前的计算系数的扩展,这种光谱的主要p-群更一般的群体。这对等变形式群律的研究具有重要意义,这是PI将追求的项目的另一部分。PI还将调查应用到她最近的计算,连同她的合作者,等变麦基Steenrod代数奇素数。具体来说,PI正在追求的一个这样的应用是构造真实的Brow-Peterson谱的奇原色版本。一个密切相关的问题是等变椭圆和Barsotti-Tate上同调的构造和理解,以及与这些谱相关的正式群律。PI还将继续她正在进行的项目,沿着与她的合作者,在自共轭和双实配边光谱的计算。这个奖项反映了NSF的法定使命,并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

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Po Hu其他文献

The mechanism of EAP-EU combined impact on summer rainfall over North Asia
EAP-EU联合影响北亚夏季降水的机制
  • DOI:
    10.1007/s00704-020-03295-0
  • 发表时间:
    2020-06
  • 期刊:
  • 影响因子:
    3.4
  • 作者:
    Po Hu;Jianbo Cheng;Guolin Feng;Muhammad Mubashar Ahmad Dogar;Zhiqiang Gong
  • 通讯作者:
    Zhiqiang Gong
LW-213 induces cell apoptosis in human cutaneous T-cell lymphomas by activating PERK–eIF2α–ATF4–CHOP axis
LW-213 通过激活 PERK–eIF2α–ATF4–CHOP 轴诱导人皮肤 T 细胞淋巴瘤细胞凋亡
  • DOI:
    10.1038/s41401-020-0466-7
  • 发表时间:
    2020-08-03
  • 期刊:
  • 影响因子:
    8.400
  • 作者:
    Xiao-xuan Yu;Meng-yuan Zhu;Jia-rong Wang;Hui Li;Po Hu;Ying-jie Qing;Xiang-yuan Wang;Hong-zheng Wang;Zhan-yu Wang;Jing-yan Xu;Qing-long Guo;Hui Hui
  • 通讯作者:
    Hui Hui
Some remarks on plectic motivic spaces and spectra
  • DOI:
    10.21136/cmj.2025.0328-24
  • 发表时间:
    2025-04-01
  • 期刊:
  • 影响因子:
    0.500
  • 作者:
    Po Hu;Daniel Kriz;Igor Kriz;Petr Somberg
  • 通讯作者:
    Petr Somberg
Experimental Study on Scouring and Silting Deformation of Artificial Beach Under Storm Surge—Wave Coupling
  • DOI:
    10.1007/s13344-022-0005-z
  • 发表时间:
    2022-02-01
  • 期刊:
  • 影响因子:
    2.200
  • 作者:
    Tian-ting Sun;Po Hu;Jun-ning Pan;Yi-jun Hou;Dong-xue Mo;Deng-ting Wang
  • 通讯作者:
    Deng-ting Wang
Qu Feng Xuan Bi Formula Alleviates Airway Inflammation and Guides Clinical Treatment by Improving Bronchial Immune Balance in the Asthma Model
祛风旋痹方通过改善哮喘模型支气管免疫平衡减轻气道炎症并指导临床治疗
  • DOI:
    10.1155/2021/6648834
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Po Hu;Suofang Shi;Li Liu;Shuomiao Yin;Lingfu Wang
  • 通讯作者:
    Lingfu Wang

Po Hu的其他文献

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{{ truncateString('Po Hu', 18)}}的其他基金

Equivariant motivic homotopy theory
等变动机同伦理论
  • 批准号:
    1104348
  • 财政年份:
    2011
  • 资助金额:
    $ 15.38万
  • 项目类别:
    Standard Grant
String-related structures in homotopy theory
同伦理论中的弦相关结构
  • 批准号:
    0503814
  • 财政年份:
    2005
  • 资助金额:
    $ 15.38万
  • 项目类别:
    Standard Grant
Geometric Aspects of Algebraic Topology
代数拓扑的几何方面
  • 批准号:
    0303505
  • 财政年份:
    2002
  • 资助金额:
    $ 15.38万
  • 项目类别:
    Standard Grant
Geometric Aspects of Algebraic Topology
代数拓扑的几何方面
  • 批准号:
    0204080
  • 财政年份:
    2002
  • 资助金额:
    $ 15.38万
  • 项目类别:
    Standard Grant
Mathematical Sciences Postdoctoral Research Fellowships
数学科学博士后研究奖学金
  • 批准号:
    9804394
  • 财政年份:
    1998
  • 资助金额:
    $ 15.38万
  • 项目类别:
    Fellowship Award

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合作研究:代数K理论、算术和等变稳定同伦理论
  • 批准号:
    2104348
  • 财政年份:
    2021
  • 资助金额:
    $ 15.38万
  • 项目类别:
    Standard Grant
Collaborative Research: Algebraic K-Theory, Arithmetic, and Equivariant Stable Homotopy Theory
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  • 批准号:
    2104420
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    2021
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球面的经典、动机和等变稳定同伦群。
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    2105462
  • 财政年份:
    2021
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    $ 15.38万
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等变稳定茎
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    2003204
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稳定同伦理论的等变和动机变形
  • 批准号:
    2005476
  • 财政年份:
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    2019
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稳定和不稳定等变色同伦的计算
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  • 财政年份:
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  • 资助金额:
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有限群和环面扩张的代数有理G-等变稳定同伦理论
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  • 财政年份:
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  • 项目类别:
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