9616630 Li This grant supports the research of Professor H. Li to work on various problems in the theory of vertex operators. He wishes to show that certain holomorphic vertex operators of degree 24 exist, to work on the rationality of some W-algebras and to establish an equivalent functor from the category of vertex algebras and the category of Poisson Lie algebras. This is research that starts out in the field of algebra but moves beyond that to touch both number theory and theoretical physics. The reasons for these connections are that algebra can be though of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively and this project will study some of these connections at length. There are also connections to coding theory and the transmission of data across communication lines.
