CAREER: Elliptic cohomology and quantum field theory

职业:椭圆上同调和量子场论

基本信息

项目摘要

The research of this award lies at the interface between theoretical physics and geometry. An unsolved conjecture posits a deep connection between the geometry of supersymmetric quantum field theories and certain structures in algebraic topology. Resolving this conjecture would provide new insight into the mathematical foundations of quantum field theory, while also providing several long-anticipated applications of algebraic topology in physics. The projects the PI will work on leverage higher categorical symmetries to gain new insights into this 30-year-old conjecture. The award supports graduate students working with the PI whose research will contribute to this area. The PI will also continue his involvement in mathematics education for incarcerated people through the Education Justice Project in Illinois.The proposed research is centered on an equivariant refinement of Stolz and Teichner’s conjectured geometric model for elliptic cohomology from 2-dimensional supersymmetric field theories. The overarching goal is to link structures in Lurie’s 2-equivariant elliptic cohomology with the geometry of supersymmetric gauge theories. Some of the projects are natural extensions of prior work at heights zero and one, focusing on height 2 generalizations of specific quantum field theories that are expected to construct elliptic Thom classes. Other projects will initiate the study of 2-equivariant geometry, interfacing with topics in string geometry, loop group representation theory, and elliptic power operations.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.
这个奖项的研究在于理论物理和几何之间的接口。一个未解的猜想假定了超对称量子场论的几何和代数拓扑中的某些结构之间的深刻联系。解决这个猜想将为量子场论的数学基础提供新的见解,同时也提供了代数拓扑在物理学中的几个期待已久的应用。PI将致力于利用更高的分类对称性来获得对这个30年前的猜想的新见解。该奖项支持与PI合作的研究生,他们的研究将有助于这一领域。PI也将继续他的参与数学教育的被监禁的人通过教育正义项目在Illinois.拟议的研究是集中在Stolz和Teichner的椭圆上同调从二维超对称场论的几何模型的等变细化。首要目标是将Lurie的2-等变椭圆上同调结构与超对称规范理论的几何结构联系起来。其中一些项目是先前工作在高度0和1的自然延伸,重点是高度2的具体量子场论的推广,预计将构建椭圆Thom类。其他项目将启动2-等变几何的研究,与弦几何,回路群表示理论和椭圆幂运算的主题相结合。该奖项反映了NSF的法定使命,并通过使用基金会的智力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(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Daniel Berwick Evans其他文献

Daniel Berwick Evans的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Daniel Berwick Evans', 18)}}的其他基金

Elliptic Cohomology, Geometry, and Physics
椭圆上同调、几何和物理
  • 批准号:
    2205835
  • 财政年份:
    2022
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Conference on Equivariant Elliptic Cohomology and Geometric Representation Theory
等变椭圆上同调与几何表示理论会议
  • 批准号:
    1903754
  • 财政年份:
    2019
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant

相似海外基金

Geometric Representations of the Elliptic Quantum Toroidal Algebras
椭圆量子环形代数的几何表示
  • 批准号:
    23K03029
  • 财政年份:
    2023
  • 资助金额:
    $ 55万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
LEAPS-MPS: Quantum Field Theories and Elliptic Cohomology
LEAPS-MPS:量子场论和椭圆上同调
  • 批准号:
    2316646
  • 财政年份:
    2023
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Elliptic Cohomology, Geometry, and Physics
椭圆上同调、几何和物理
  • 批准号:
    2205835
  • 财政年份:
    2022
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Conference on Equivariant Elliptic Cohomology and Geometric Representation Theory
等变椭圆上同调与几何表示理论会议
  • 批准号:
    1903754
  • 财政年份:
    2019
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Derived Geometry, Elliptic Cohomology, and Loop Stacks
导出几何、椭圆上同调和循环堆栈
  • 批准号:
    1714273
  • 财政年份:
    2017
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Twists of elliptic cohomology and K-theory
椭圆上同调和 K 理论的扭曲
  • 批准号:
    1104746
  • 财政年份:
    2011
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Interactions of Elliptic Cohomology with Other Subjects
椭圆上同调与其他学科的相互作用
  • 批准号:
    0754204
  • 财政年份:
    2007
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Field Theories and Elliptic Cohomology
场论和椭圆上同调
  • 批准号:
    0707068
  • 财政年份:
    2007
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
Elliptic cohomology and the enumerative geometry of elliptic Calabi-Yau manifolds : Towards the understanding of string dualities
椭圆上同调和椭圆卡拉比-丘流形的枚举几何:理解弦对偶性
  • 批准号:
    19540024
  • 财政年份:
    2007
  • 资助金额:
    $ 55万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Interactions of Elliptic Cohomology with Other Subjects
椭圆上同调与其他学科的相互作用
  • 批准号:
    0504539
  • 财政年份:
    2005
  • 资助金额:
    $ 55万
  • 项目类别:
    Standard Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了