讲座题目：Modular invariance of (logarithmic) intertwining operators
主讲人：黄一知 教授
主持人：罗栗 教授
开始时间：2023-06-29 13:00
讲座地址：数学楼126
主办单位：数学科学学院
报告人简介：
黄一知，美国罗格斯大学教授,主要从事量子场论的数学理论及其在代数、几何、拓扑、弦论和凝聚态物理中的应用，其中的代表性研究工作包括建立公理化的顶点算子代数的定义，顶点算子代数的张量范畴理论的研究，顶点算子代数框架下一般形式的Verlinde猜想的证明等。在Duke Math. J.、Comm. Math. Phys.、Trans. Amer. Math. Soc.、Selecta Math.等著名期刊发表高水平学术论文，其中包括一本Mem. Amer. Math. Soc.专著，被同行文章引用超2000篇次，并担任国际知名数学杂志Commun. Contemp. Math.主编以及SCI杂志New York J. Math.编委。
报告内容：
I will discuss a proof of a conjecture of almost twenty years on the modular invariance of (logarithmic) intertwining operators. Let V be a C_2-cofinite vertex operator algebra without nonzero elements of negative weights. The conjecture states that the vector space spanned by pseudo-q-traces shifted by -c/24 of products of (logarithmic) intertwining operators among grading-restricted generalized V-modules is a module for the modular group SL(2, Z). In 2015, Fiordalisi proved that such pseudo-q-traces are absolutely convergent and have the genus-one associativity property and some other properties. Recently, I have proved this conjecture completely. This modular invariace result gives a construction of C_2-cofinite genus-one logarithmic conformal field theories. We expect that it will play an important role in the study of problems and conjectures on C_2-cofinite logarithmic conformal field theories.
