Two-dimensional conformal field theories and their moduli space.

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。在过去的几年里，黄教授证明了Verlinde猜想和Verlinde公式，这两个猜想和公式在共形场论及相关学科中起着基础性的作用，并证明了满足一定自然条件的顶点算子代数的模的带状范畴的刚性和模性。他调查了其他问题的数学基础的二维共形场理论。他的兴趣是解决该领域中一些尚未解决的难题。Huang提出的研究预计将在一般的orbifold共形场论和高阶亏格共形场论上给出结果，对某些orbifold共形场论和某些Calabi-Yau流形之间的联系的数学理解，共形场论变形的数学理论的坚实基础，更好地理解与共形场论有关的卡-丘流形几何，并对物理学中的数学基础问题有新的认识。更广泛的影响来自PI的教学，指导，咨询，演讲，论文写作，会议组织，会议组织，卷编辑和其他此类活动。特别是，他将继续投入大量时间培养REU本科生和博士。学生黄将继续鼓励妇女和代表性不足的少数群体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，黄还对将他的结果和方法应用于物理问题感兴趣，例如与量子计算和弦理论有关的问题。

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.