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

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年美国复苏和再投资法案（公法111-5）资助的。近年来，Huang证明了在共形场论及相关学科中起基础作用的Verlinde猜想和Verlinde公式，并证明了满足一定自然条件的顶点算子代数的带状模类的刚性和模性。他还研究了二维共形场论的数学基础中的其他问题。他的兴趣在于解决该领域一些尚未解决的难题。黄教授的研究有望在一般的轨道共形场论和高格共形场论方面取得成果，对某些轨道共形场论和某些Calabi-Yau流形之间关系的数学理解，为共形场论变形的数学理论奠定坚实的基础。更好地理解与共形场理论相关的Calabi-Yau流形的几何形状，并对物理学中潜在的数学问题有了新的认识。更广泛的影响来自PI的教学、指导、咨询、演讲、说明文写作、会议组织、研讨会组织、卷编辑和其他此类活动。特别是，他将继续投入大量的时间来培养REU的本科生和博士生。黄教授将继续鼓励女性和少数族裔成员参与他们的研究领域。除了研究二维共形场论的理论方面，黄还对寻找他的结果和方法在物理问题上的应用感兴趣，例如与量子计算和弦理论相关的问题。