報(bào)告題目：Representation and tensor category of affine sl_2 at positive rational levels

　　報(bào)告人：楊進(jìn)偉教授（上海交通大學(xué)）

　　時(shí) 間：2025年6月19日 10:00-11:00

　　地點(diǎn)：理學(xué)院1號樓1-301

　　摘要：In a series of celebrated work, Kazhdan and Lusztig constructed braided tensor category structure on the category of finite length modules for the 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 and prove rigidity in some cases. For affine sl_2 Lie algebra, we also study 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.

　　報(bào)告人簡介：楊進(jìn)偉，上海交通大學(xué)副教授，本科和碩士畢業(yè)于北京大學(xué)數(shù)學(xué)學(xué)院，師從張繼平院士，2014年在羅格斯大學(xué)取得博士學(xué)位，導(dǎo)師為黃一知教授。他的主要研究領(lǐng)域?yàn)槔罾碚摚硎菊摵蛷埩糠懂犂碚摚绕涫怯庙旤c(diǎn)算子代數(shù)的張量范疇理論來研究李代數(shù)、量子群、頂點(diǎn)算子代數(shù)等代數(shù)對象的表示和張量范疇結(jié)構(gòu)及其對應(yīng)關(guān)系。主要研究成果發(fā)表在Math. Ann., Adv. Math., Comm. Math. Phys., IMRN等期刊上。