Vertex operator algebras, conformal blocks, and tensor categories

Time:2022.2.21~5.13 (Mon. /Thurs. ) 19:20-20:55

Venue:Zoom Meeting ID: 361 038 6975 Passcode: BIMSA Offline:近春西楼报告厅 Lecture Hall





Vertex operator algebras (VOAs) are mathematical objects describing 2d chiral conformal field theory. The representation category of a “strongly rational” VOA is a modular tensor category (which yields a 3d topological quantum field theory), and conjecturally, all modular tensor categories arise from such VOA representations. Conformal blocks are the crucial ingredients in the representation theory of VOAs.

This course is an introduction to the basic theory of VOAs, their representations, and conformal blocks from the complex analytic point of view. Our goal in the first half of this course is to get familiar with the computations in VOA theory and some basic examples. The second half is devoted to the study of conformal blocks. The goal is to understand the following three crucial properties of conformal blocks and the roles they play in the representation categories of VOAs. (1) The space of conformal blocks forms a vector bundle with (projectively flat) connections. (2) Sewing conformal blocks is convergent (3) Factorization property.

I will type lecture notes and post them on my website


Complex analysis, differential manifolds, basic notions of Lie algebras

DATEMarch 14, 2022
Related News
    • 0

      Topics on modular tensor categories

      PrerequisiteGraduate level algebra.AbstractIn this course, we first introduce the notion modular tensor categories, and briefly explain how they are related to many areas of mathematics and physics. Then we will focus on the algebraic properties of MTC, mainly from their rationality, Galois symmetry and congruence properties.Lecturer Intro.Yilong Wang graduated from The Ohio State University in...

    • 1

      Brief Introduction to Tensor Network algorithms

      IntroductionThis course will focus on the basic concepts and representative algorithms of tensor networks. For 1D tensor networks, we will introduce the Matrix Product State(MPS) and its Density Matrix Renormalization Group algorithm(DMRG), Time Evolution Block Decimation algorithm(TEBD), etc. For high-dimensional tensor networks, we will include the Projected Entangled Pair States (PEPS) and i...