EAPSI: Understanding the Integral Forms of Vertex Operator Algebras and their Applications in Theoretical Physics

EAPSI:理解顶点算子代数的积分形式及其在理论物理中的应用

基本信息

  • 批准号:
    1614336
  • 负责人:
  • 金额:
    $ 0.54万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Fellowship Award
  • 财政年份:
    2016
  • 资助国家:
    美国
  • 起止时间:
    2016-06-15 至 2017-05-31
  • 项目状态:
    已结题

项目摘要

The theory of vertex operator algebras is a mathematical framework whose importance reaches well outside of mathematics. It is prevalent in theoretical physics, in particular, conformal field theory and string theory, which attempts to provide a unified description of all the forces of nature. While a vertex operator algebra is most often considered over the field of complex numbers or fields of characteristic zero, little is known about those over a field of prime characteristic p. Integral forms are known to bridge this gap and are precisely the primary interest of this project. A better understanding of vertex operator algebras over fields of prime characteristic plays an important role in the study of modular representations of finite groups, rational vertex operator algebras, and rational conformal field theory. The project will be conducted at the School of Mathematics at Sichuan University under the mentorship of Prof. Li Ren. Prof. Ren, who specializes in vertex operator algebras. Prof. Ren is a coauthor of a manuscript regarded as the first paper dealing with modular vertex operator algebras.This project aims to answer the question: When does a vertex operator algebra have an integral form? In this branch of mathematics, rationality and C2-cofiniteness are among the most important concepts. The research will investigate the conjecture that if V is a rational, C2-cofinite, and self-dual simple vertex operator algebra, then V has an integral form. Professor Ren's recent works include new results on the representations of vertex operator algebras over an arbitrary field, not just fields of characteristic zero. This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and China's Ministry of Science and Technology.
顶点算子代数理论是一个数学框架,其重要性远远超出了数学。它在理论物理学中很普遍,特别是共形场论和弦理论,它们试图提供自然界所有力的统一描述。虽然顶点算子代数是最经常考虑的领域的复数或领域的特征零,鲜为人知的是那些领域的主要特征p.积分形式是已知的桥梁这一差距,正是主要利益的这一项目。更好地理解素特征域上的顶点算子代数在有限群的模表示、有理顶点算子代数和有理共形场论的研究中起着重要的作用。该项目将在四川大学数学学院进行,导师为李仁教授。研究顶点算子代数的任教授。 任教授是一篇手稿的合著者,该手稿被认为是第一篇涉及模顶点算子代数的论文。该项目旨在回答以下问题:顶点算子代数何时具有积分形式?在这一数学分支中,合理性和C ~ 2-有限性是最重要的概念。研究了一个猜想:如果V是有理的、C2-上有限的、自对偶的单顶点算子代数,则V有积分形式。任教授最近的工作包括新的结果表示顶点算子代数在任意领域,而不仅仅是领域的特征零。该奖项属于东亚和太平洋夏季研究所项目,支持美国研究生的夏季研究,由NSF和中国科技部共同资助。

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 }}

Danquynh Nguyen其他文献

Fusion Rules among θ-Twisted Modules for Lattice Vertex Operator Algebras VL
点阵顶点算子代数 VL 的 θ 扭曲模块之间的融合规则
  • DOI:
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Danquynh Nguyen
  • 通讯作者:
    Danquynh Nguyen
Fusion Rules for the Lattice Vertex Operator Algebra $V_L$
晶格顶点算子代数 $V_L$ 的融合规则
  • DOI:
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Danquynh Nguyen
  • 通讯作者:
    Danquynh Nguyen

Danquynh Nguyen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('Danquynh Nguyen', 18)}}的其他基金

EAPSI: Modular Vertex Operator Algebras Associated with the Virasoro Algebra
EAPSI:与 Virasoro 代数相关的模顶点算子代数
  • 批准号:
    1713945
  • 财政年份:
    2017
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Fellowship Award

相似国自然基金

Understanding structural evolution of galaxies with machine learning
  • 批准号:
  • 批准年份:
    2022
  • 资助金额:
    10.0 万元
  • 项目类别:
    省市级项目
Understanding complicated gravitational physics by simple two-shell systems
  • 批准号:
    12005059
  • 批准年份:
    2020
  • 资助金额:
    24.0 万元
  • 项目类别:
    青年科学基金项目

相似海外基金

Proton, alpha and gamma irradiation assisted stress corrosion cracking: understanding the fuel-stainless steel interface
质子、α 和 γ 辐照辅助应力腐蚀开裂:了解燃料-不锈钢界面
  • 批准号:
    2908693
  • 财政年份:
    2027
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Studentship
Understanding the interplay between the gut microbiome, behavior and urbanisation in wild birds
了解野生鸟类肠道微生物组、行为和城市化之间的相互作用
  • 批准号:
    2876993
  • 财政年份:
    2027
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Studentship
Understanding how pollutant aerosol particulates impact airway inflammation
了解污染物气溶胶颗粒如何影响气道炎症
  • 批准号:
    2881629
  • 财政年份:
    2027
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Studentship
Understanding and Improving Electrochemical Carbon Dioxide Capture
了解和改进电化学二氧化碳捕获
  • 批准号:
    MR/Y034244/1
  • 财政年份:
    2025
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Fellowship
Understanding The Political Representation of Men: A Novel Approach to Making Politics More Inclusive
了解男性的政治代表性:使政治更具包容性的新方法
  • 批准号:
    EP/Z000246/1
  • 财政年份:
    2025
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Research Grant
Home helper robots: Understanding our future lives with human-like AI
家庭帮手机器人:用类人人工智能了解我们的未来生活
  • 批准号:
    FT230100021
  • 财政年份:
    2025
  • 资助金额:
    $ 0.54万
  • 项目类别:
    ARC Future Fellowships
Deep imaging for understanding molecular processes in complex organisms
深度成像用于了解复杂生物体的分子过程
  • 批准号:
    LE240100091
  • 财政年份:
    2024
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Linkage Infrastructure, Equipment and Facilities
Understanding the implications of pandemic delays for the end of life
了解大流行延迟对生命终结的影响
  • 批准号:
    DP240101775
  • 财政年份:
    2024
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Discovery Projects
Understanding multiday cycles underpinning human physiology
了解支撑人体生理学的多日周期
  • 批准号:
    DP240102899
  • 财政年份:
    2024
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Discovery Projects
Understanding T cell trafficking and function during antigenic interference
了解抗原干扰期间 T 细胞的运输和功能
  • 批准号:
    DP240101665
  • 财政年份:
    2024
  • 资助金额:
    $ 0.54万
  • 项目类别:
    Discovery Projects
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了