报告题目 (Title)：（对数）缠结算子的模不变性（Modular invariance of (logarithmic) intertwining operators）

报告人 (Speaker)： 黄一知 教授（美国Rutgers大学)

报告时间 (Time)：2023年6月27日 (周二) 16:00-17：00

报告地点 (Place)：校本部F309

邀请人(Inviter)：张红莲 教授

主办部门：理学院数学系

报告摘要： 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 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. The talk will start with the meaning of modular transformations and the definition of vertex operator algebras.