报告时间：10月20日周一下午16:00-17:00
报告地点：数学楼401报告厅
报告人：杨进伟
主持人：胡乃红
报告摘要：
In a series of celebrated work, Kazhdan and Lusztig constructed braided tensor category structure on the representation categories of affine Lie algebras when the level plus dual Coxeter number is not a postive rational number, and proved that the category is equivalent to the category of quantum groups at the corresponding parameter. In this talk, we discuss our recent progress on tensor categories at postive rational levels using vertex operator algebra approach. Concretely, We construct braided tensor category structure on the category of ordinary modules for simple affine vertex operator algebras at admissible levels. For affine sl_2 Lie algebra, we also study two bigger representation categories at admissible levels, one is the category of weight modules for the simple affine vertex operator algebra, which is neither finite or semisimple, we prove its rigidity, the other is the category of finite length generalized modules for the universal affine vertex operator algebra, we show this category is derived equivalent to the category of the quantum groups at the corresponding parameter. This is based on a series of joint work with T. Creutzig, Y.-Z. Huang and R. McRae.
报告人简介：
杨进伟，上海交通大学副教授，国家高层次青年人才（海优）。2014年在罗格斯大学跟随VOA及张量范畴著名专家黄一知教授取得博士学位，博士后分别在美国的Notre Dame三年，Yale一年，加拿大的Alberta三年。主要研究领域为顶点算子代数及其表示论、modular张量范畴理论。在Proc. LMS, Adv. Math., Comm. Math. Phys., Trans AMS, Math. Ann., IMRN, CCM等著名期刊上发表论文34篇。