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

李代数、顶点算子代数及其应用；

• 批准号: 0453004
• 负责人: Kailash Misra
• 金额: --
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0453004&HistoricalAwards=false
• 关键词: Lie; Algebras; Vertex; Operator; Their

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.

有限和无限维度的Lie代数理论一直是数学研究的主要领域，在许多其他数学和物理学领域中有许多应用，例如，组合学，组理论，数量理论，部分微分方程，拓扑，拓扑，拓扑结构，拓扑结构，完美的场理论和弦乐理论，统计力学和可集成的系统。特别是，一类重要的无限尺寸谎言代数的表示理论被称为主载体代数，导致了新的代数结构的发现，例如顶点（操作员）代数和量子组。这两种代数结构已成为当前数学研究的重要领域，与数学和物理学的许多其他领域有着深厚的联系。 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对于数字理论，组合，形式的野外理论和统计力学。lie代数是描述连续对称性的一类代数。它们是由数学家S. Lie首先在当时介绍的，自那时以来，许多著名的数学家和物理学家都对它们进行了研究。 在二十世纪，莱尔奇布拉群岛的理论迅速发展为主要研究领域的inmapshematics，具有许多重要的物理学应用。脊椎动物代数和量子组是相对较新的代数类，可以看作是Lie代数的深远类似物。顶点操作员代数已用于解决与离散对称性和数字理论相关的问题。它们也是描述现象的形成理论中的重要成分，例如在该现象中，冰，冰和蒸汽共存的物理状态以及称为弦乐理论的物理理论，某些物理学家用来统一了Universe中的所有力量。这次会议是在Vertex操作员代数和应用程序的Lie代数上进行的，它将鼓励数学家和物理学家进行互动，并联合起来以发现Discovernew Frontiers。这对于毕业的毕业生和初级教职员工将尤其有益。我们将鼓励研究生，初级研究人员，妇女，少数民族和残疾人的参与，以优先获得财政支持。