This project is to support US participants' travel to the international conferences on Vertex Algebra and Related Topics which will be held in Kyoto during December 15-17, 2010 and Taipei in December of 2011. The conferences cover the following topics: infinite dimensional Lie algebras, vertex algebras, representation theory, number theory, combinatorics, group theory, and connections among vertex algebras, conformal nets and conformal field theory. The major goal of the proposed conferences is to present the most important developments in vertex algebras.
The proposed conferences help to maintain the international standing of the American researchers in the theory of vertex algebra. The proposed activities have a strong impact on educating and training young mathematicians. Graduate students and junior researchers (some of them are from non Ph.D. institutions) will be invited to attend the conferences and to give talks. The conference will also help to strength the communication and cooperation among different schools.
Vertex operator algebras appear as symmetries of two demensional conformal field theory. The theory of vertex algebras have developedrapidly during the three two decades. This development has various applications to many branches in mathematics and physics such as integrable system, topology, geometry, number theory, conformal field theory and string theory. This grant from the NSF supported American mathematicians to attend international conferences on vertex operator algebras and related topics held in Japan, Taiwan, China. The American mathematicians presented their research results in these conferences and also learned from the experts from the other countries. These conferences also provided opportunities for young mathematicians to collaborate with leading experts in vertex algebras, to learn the most important development in the field, and to show off their accomplishments in front of the international leaders in the area. The conferences have helped reserachers to have a better understanding on the structure and representation theory of vertex operator algebras, and have led the recent advances in the study of quantum dimensions, classification of holomorphic vertex operator algebras with central charge 24, orbifold theory and coset theory. The conferences have helped reserachers to have a better understanding on two dimensional conformal field theory in physics. The confereces also strengthened the research communications and cooperations obetween American mathematicans and experts from the other countries.
