This project is concerned with infinite dimensional Lie algebras, their representations and their connections with mathematical physics. The principal investigator will formulate recent work of Macdonald and Stanley on symmetry polynomials in terms of vertex operators in an effort to obtain the local theory needed for formulating quantum field theory on an arithmetic surface. He will also study the cohomology of the mapping class group. The research supported concerns an important focus of current mathematical activity, where group representation theory, quantum field theory, and algebraic geometry all come together. This work has important implications for theoretical physics as well as several areas of mathematics.
