Modular invariance of characters of a rational conformal field theory has been known since the work of Cardy, and it was proved by Zhu for rational and C_2-cofinite vertex operator algebras (VOA), which constitute a mathematical formalization of RCFT. This talk will discuss the modularity of trace functions in rational orbifold theory. We will also propose how to use the modularity to characterize the rationalilty of vertex operator algebras.

报告人简介：董崇英，美国加州大学Santa Cruz分校讲席教授，美国数学会会士，国家杰出青年基金获得者，“长江学者”讲座教授，主要从事顶点算子代数和无穷维李代数的研究。他在顶点算子代数、Orbifold理论和广义月光猜想等方向做出了重要的贡献，已在Acta. Math., Duke. Math. J., Amer. J. Math., Crelle's Journal, Com. Math. Phys.等期刊发表学术论文120多篇，相关成果被引用7800多次。