Seminars & Colloquia Calendar
Modular invariance of logarithmic intertwining operators
Speaker Yi-Zhi Huang, Rutgers University
Location: Hill 705
Date & time: Friday, 28 April 2023 at 12:10PM - 1:10PM
Abstract I will discuss a proof of the conjecture of almost twenty years on the modular invariance of (logarithmic) intertwining operators.Let V be a C_2-cofinite vertex operator algebra of positive energy.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 gives a construction of C_2-cofinite genus-one logarithmic conformal field theories. It might play an important role in the future proofs of the conjectures on the corresponding braided tensor categories, especially their rigidity and modularity.