主讲人：黄一知 教授（美国罗格斯大学）

时间：2014年6月11日（周三）16:00-17:00

地点：必赢76net线路官网北二区教学楼 510 教室

摘要：In this talk I will survey the modular invariance results and conjectures in conformal field theory.

In 1988, in a pioneering work of Moore and Seiberg, a modular invariance conjecture for chiral vertex operators (intertwining operators) in rational conformal field theories was formulated and was used to derive the important Moore-Seiberg polynomial equations, which in turn were used to show that the Verlinde conjecture follows from some basic conjectures on rational conformal field theories, including, in particular, the modular invariance conjecture. In 1990, in an important work of Zhu, a partial result on the modular invariance conjecture of Moore and Seiberg was obtained. However, Zhu's method cannot be used or adapted to prove the full modular invariance conjecture of Moore and Seiberg. In 2003, using a method involving modular invariant differential equations and operator product expansions, I proved this modular invariance conjecture. With the discovery of fatal gaps and mistakes in the claimed constructions of conformal-field-theoretic structures, the importance of this theorem becomes more and more apparent. In 2006, in a joint work with Kong, I proved further the modular invariance of full rational conformal field theories. In the case of logarithmic conformal field theories, Miyamoto in 2002 generalized Zhu's partial result to a corresponding partial result with an additional assumption on irreducible modules. Several years ago, I formulated a full modular invariance conjecture for logarithmic intertwining operators. In the thesis work of Fiordalisi, substantial progress has been made on this modular invariance conjecture.

I will discuss the historical development and mathematical significance of the modular invariance results and conjectures mentioned above.