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 the discovery 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 field theory and statistical mechanics.
Lie algebras are a class of algebras describing continuous symmetries in nature. They were first introduced by mathematician S. Lie in the ninteenth century and have been studied by many prominent mathematicians and physicists since then. During the twentieth century, the theory of Lie algebras developed rapidly into a main research area in mathematics with numerous important applications in physics. Vertex operator 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 a physical theory describing phenomena such as the physical state in which water, ice and steam coexist and in a physical theory called string theory which some physicists are using to unify all the forces in the universe. This conference is on Lie algebras, vertex operator algebras and their applications and it will encourage mathematicians and physicists to interact and, to join forces to discover new frontiers. It will be especially beneficial to graduate students and junior faculty members who have just 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.
