In recent years, a new connection between mathematics and string theory of physics has been discovered. This project is concerned with studying certain infinite dimensional Lie algebras which play an important role in this connection. These Lie algebras will be considered from a geometric point of view. The objective is to apply the method of string path integrals in physics to the representation theory of affine Kac-Moody algebras and so-called vertex operator algebras. This research is concerned with a mathematical object called a Lie algebra. Lie algebras arise from another object called a Lie group. An example of a Lie group is the set of rotations of a sphere where one rotation is followed by another. Lie groups and Lie algebras are important in areas involving analysis of spherical motion.
