Modular invariance of (logarithmic) intertwining operators

：黄一知（美国罗格斯大学）
：2023-06-15 16:30
：海韵园实验楼105报告厅

报告人：黄一知（美国罗格斯大学）

时  间：2023年6月15日16:30

地  点：海韵园实验楼105报告厅

内容摘要:

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 invariance 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 several conjectures on C_2-cofinite logarithmic conformal field theories, including, in particular, the rigidity and modularity of the corresponding braided tensor categories.

个人简介：

黄一知，美国罗格斯（Rutgers）大学教授。主要研究兴趣是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。他是数学期刊Communications in Contemporary Mathematics主编以及New York Journal of Mathematics编委会成员。

联系人：王清