Kernel Functions, Analytic Torsion, and Moduli Spaces

This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.