Lie Algebras, Vertex Operator Algebras and Their Applications; May 17-21, 2005; Raleigh, NC

有限和无限维李代数理论一直是数学研究的主要领域，在数学和物理的许多其他领域都有许多应用，例如组合学、群论、数论、偏微分方程组、拓扑学、保形场论和弦理论、统计力学和可积系统。特别是，一类被称为仿射李代数的无穷维李代数的表示理论导致了新的代数结构的发现，如顶点(算子)代数和量子群。这两种代数结构都已经成为当前数学研究的重要领域，与数学和物理学中的许多其他领域有着深刻的联系。这次会议将为从事李代数、顶点算符代数及其应用领域的数学和物理研究人员探索21世纪可能的新研究方向提供一个极好的环境。会议的焦点将集中在以下主题：(I)有限和无限维李代数和量子群。(Ii)顶点算符代数及其表示。(Iii)在数论、组合学、共形场理论和统计力学中的应用。Lie代数是一类描述自然界中连续对称的代数。它们最早是由数学家S·李在9世纪提出的，从那时起，许多著名的数学家和物理学家都在研究它们。在二十世纪，李代数理论迅速发展成为数学的一个主要研究领域，在物理学中有许多重要的应用。顶点算子代数和量子群是一类相对较新的代数，可以看作是李代数的深远类似物。顶点算子代数被用来解决与离散对称和数论有关的问题。它们也是描述水、冰和蒸汽共存的物理状态等现象的形而上学理论的重要组成部分，也是一些物理学家用来统一宇宙中所有力的称为弦理论的物理理论的重要组成部分。这次会议是关于李代数、顶点算子代数及其应用的会议，它将鼓励数学家和物理学家相互作用，并联合起来发现新的前沿。这对刚毕业的学生和刚刚开始他们职业生涯的初级教职员工尤其有益。鼓励研究生、初级科研人员、妇女、少数民族和残疾人参与，给予优先资助。

The theory of Lie algebras, both finite and infinite-dimensional, have been a major area of mathematical research with numerous applications in many other areas of mathematics and physics, for example, combinatorics, group theory, number theory, partial differential equations, topology, conformal field theory and string theory, statistical mechanics and integrable systems. In particular, the representation theory of an important class of infinite dimensional Lie algebras known as affine Lie algebras has led to thediscovery of new algebraic structures, such as vertex (operator) algebras and quantum groups. Both of these algebraic structures have become important areas of current mathematical research with deep connections with many other areas in mathematics and physics. This conference will provide an excellent setting for researchers in mathematics and physics working in the area of Lie algebras, vertex operator algebras and their applications to explore possible new directions of research in the twenty-first century.The focus of the conference will be on the following topics:(i) Finite and infinite dimensional Lie algebras and quantum groups.(ii) Vertex operator algebras and their representations.(iii) Applications to number theory, combinatorics, conformal fieldtheory and statistical mechanics.Lie algebras are a class of algebras describing continuous symmetries innature. They were first introduced by mathematician S. Lie in theninteenth century and have been studied by many prominent mathematicians andphysicists since then. During the twentieth century, the theory of Liealgebras developed rapidly into a main research area inmathematics with numerous important applications in physics. Vertexoperator algebras and quantum groups are relatively new class of algebras and can be viewed as far-reaching analogues of Lie algebras. Vertex operator algebras have been used to solve problems related to discrete symmetries and to number theory. They are also an important ingredient in aphysical theory describing phenomena such as the physical state in whichwater, ice and steam coexist and in a physical theory called stringtheory which some physicists are using to unify all the forces in theuniverse. This conference is on Lie algebras, vertex operator algebrasand their applications and it will encourage mathematicians andphysicists to interact and, to join forces to discovernew frontiers. It will be especially beneficial to graduatestudents and junior faculty members who havejust started their careers. We will encourage participation from graduate students, junior researchers, women, minorities, and persons with disabilities by giving them priority for financial support.