Two-dimensional conformal field theories and their moduli space.

二维共形场论及其模空间。

• 批准号: 0901237
• 负责人: Yi-Zhi Huang
• 金额: $ 27.55万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901237&HistoricalAwards=false
• 关键词: Two; dimensional; conformal; field; theories; Two; dimensional; conformal; field; theories

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).In the last few years, Huang has proved the Verlinde conjecture and the Verlinde formula which play a fundamental role in Conformal Field Theory and related subjects and has proved the rigidity and modularity of the ribbon category of modules for vertex operator algebras satisfying certain natural conditions. He has investigated other problems in the mathematical foundation of two-dimensional conformal field theory. His interest is in tackling some of the still-unsolved hard problems in that field. The proposed research of Huang is expected to give results on general orbifold conformal field theories and higher-genus conformal field theories, a mathematical understanding of the connection between certain orbifold conformal field theories and certain Calabi-Yau manifolds, a solid foundation to a mathematical theory of deformations of conformal field theories, a better understanding of the geometry of Calabi-Yau manifolds related to conformal field theories and new insight into the mathematics underlying problems in physics. Broader impacts arise from the PI's teaching, mentoring, advising, lecturing, expository writing, conference-organizing, seminar-organizing, volume-editing and other such activities. In particular, he will continue to devote a large amount of time to train REU undergraduate students and Ph.D. students. Huang will continue to encourage the participation of women and members of underrepresented minority groups in their areas of study. Besides studying the theoretical aspects of two-dimensional conformal field theory, Huang is also interested in finding applications of his results and approaches to problems in physics, such as problems related to quantum computing and string theory.

该奖项是根据2009年的《美国复苏与重新投资法》（公法111-5）资助的。在过去的几年中，黄已证明了Verlinde的猜想和Verlinde公式，而Verlinde公式在整形野外理论和相关主题中起着基本作用，并且证明了模量cerse for Verege for vertex perteders Albrbrbrarb albrbr a and corpory crision corpery的刚性和模块化。他研究了二维形成综合场理论的数学基础中的其他问题。他的兴趣是解决该领域中一些尚未解决的困难问题。 The proposed research of Huang is expected to give results on general orbifold conformal field theories and higher-genus conformal field theories, a mathematical understanding of the connection between certain orbifold conformal field theories and certain Calabi-Yau manifolds, a solid foundation to a mathematical theory of deformations of conformal field theories, a better understanding of the geometry of Calabi-Yau manifolds related to conformal field theories and new深入了解物理学中潜在问题的数学。 PI的教学，指导，建议，讲课，会议组织，研讨会组织，数量编辑和其他此类活动产生了更大的影响。特别是，他将继续花费大量时间来培训REU本科生和博士学位。学生。黄将继续鼓励妇女和代表性不足的少数群体的参与。除了研究二维综合场理论的理论方面外，黄还有兴趣寻找其结果的应用和物理问题的方法，例如与量子计算和弦理论有关的问题。