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

• 批准号: 1614336
• 负责人: Danquynh Nguyen
• 金额: $ 0.54万
• 依托单位: Nguyen Danquynh T
• 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
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1614336&HistoricalAwards=false
• 关键词: EAPSI; Understanding; Integral; Forms; Vertex

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。