报告简介：
A main theme in the development of the theory of vertex operator algebras (VOAs) is the factorization property. If $V$ is a $C_2$-cofinite rational VOA (which corresponds to the chiral algebra of a rational CFT in physics), the factorization property---saying roughly that higher genus conformal blocks can be decomposed into lower genus ones---was recently completely proved. Its low genus special cases (such as Zhu's modular invariance theorem in 1996 and Huang's associativity theorem for intertwining operators in 2005) are crucial to the understanding of the representation theory of $V$. This talk focuses on $C_2$-cofinite VOAs that are not necessarily rational. Such VOAs correspond to chiral algebras of finite-type logarithmic CFTs. Since their representation categories are not necessarily semisimple, the study of their conformal blocks differ significantly from the rational case. In this talk, I will present my recent joint work with Hao Zhang on the complete proof of the factorization property for conformal blocks of such VOAs. We will also discuss the natural associative algebras in log CFT that play the role of Zhu's algebra in rational CFT. In particular, we show that the 0-th order Hochschild cohomology of that algebra is isomorphic to the space of torus conformal blocks. This is based on our works arXiv:2503.23995 and arXiv:2508.04532.

主讲人简介：
归斌，清华大学丘成桐数学中心助理教授。2018年8月在Vanderbilt University获得博士学位。2018-2021在Rutgers University做博士后。主要研究兴趣为顶点算子代数，以及与其相关的泛函分析与算子代数、张量范畴等问题。研究成果发表在《Communications in Mathematical Physics》, 《Transactions of AMS》, 《International Mathematics Research Notices》等国际期刊。