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报告题目：Modular invariance of (logarithmic) intertwining operators

报告人：Professor Yi-Zhi Huang (Rutgers University)

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. This talk will start with the meaning of modular transformations and the definition of vertex operator algebras.

报告时间：2023年7月11日（周二）上午10:30-11:30

报告地点：校本部教二楼808教室

邀请人：戎小春、胥世成