During this semester we will have a weekly seminar on representation theory of vertex algebras, as a preparation for the trimester program in 2020. We will cover among others the following articles
•Y. Zhu. Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc., 9(1):237–302, 1996• I. Frenkel and Y. Zhu. Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Mathematical Journal,66(1):123–168, 1992• C. Dong, H. Li, and G. Mason. Vertex operator algebras and associativealgebras. Journal of Algebra, 206:67–96, 1998• Y.-Z. Huang and J. Yang. On functors between module categories for associative algebras and for N-graded vertex algebras. Journal of Algebra, 409:344–361, 2014• M. Miyamoto. Modular invariance of vertex operator algebras satisfying c2-cofiniteness condition. Duke Mathematical Journal, 122:51–91, 2004• Y.-Z. Huang and J. Yang. Associative algebras for (logarithmic) twisted modules for a vertex operator algebra. Transactions of the American Mathematical Society, 371:3747–3786, 2019• Y.-Z. Huang. Differential equations, duality and modular invariance. Communications in contemporary mathematics, 7:649–706, 2005 • X. He. Higher level Zhu algebras are subquotients of universal enveloping algebras.