This project is concerned with quantum field theory on a Riemann surface and the information that this will shed on automorphic forms, the index theorem and finite simple groups. The principal investigator will endeavor to obtain the Quillen metric for the determinant line bundle for holomorphic vector bundles on a compact Riemann surface by means of representation theory. Further, he will continue to explore the arithmetric theory of loop groups and loop group monopoles. The research supported is at 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 for several areas of mathematics.
