Vertex operator algebras and their representations短课程

：David Ridout（澳大利亚University of Melbourne）
：2025-11-24 ——2025-11-27
：海韵园实验楼S307

一、授课日期

2025年11月24日——11月27日

 

二、地点

上课地点：厦门大学海韵园实验楼S307

 

三、课程介绍  

（一）课程内容简介

This is a quick introduction to some of the most important vertex-operator algebras (VOAs), the affine ones, and their representation theories. Throughout, I will illustrate any generalities with examples based on $\mathfrak{sl}_2$, $\mathfrak{sl}_3$ and (if time permits) $\mathfrak{osp}_{1\vert2}$. 

 

（二）授课老师

David Ridout（University of Melbourne）

 

（三）授课老师简介

David Ridout is a mathematical physicist, specialising in the representation theory of vertex-operator (super) algebras, particularly in the nonsemisimple case. This area is not only relevant to theoretical physics (d=2 conformal field theory and dualities with d>2 gauge theories), it also impacts many areas of pure mathematics including number theory (mock/quantum modular forms), combinatorics (generalised q-series) and category theory (modular tensor categories).

 

四、课程安排

授课日期	授课时间	教学内容纲要
11月24日	09:00-12:00	What is a vertex-operator algebra (VOA)? We motivate VOAs and how to work with them through affine examples.
11月25日	15:00-18:00	Representation theory of VOAs. We introduce the Zhu algebra of a VOA and give some examples. This leads to relaxed highest-weight modules and spectral flows.
11月26日	15:00-18:00	Classifications via coherent families. We recall Mathieu's notion of a coherent family and how it relates to the classification of relaxed highest-weight (affine) VOA-modules.
11月27日	15:00-18:00	Inverse quantum hamiltonian reduction. We outline quantum hamiltonian reduction and W-algebras before explaining the new "inverse reduction" paradigm for constructing relaxed highest-weight VOA-modules.

 

五、联系人

刘老师，tymath1@xmu.edu.cn，0592-2580036