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. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.Fay, John is the author of 'Kernel Functions, Analytic Torsion, and Moduli Spaces' with ISBN 9780821825501 and ISBN 082182550X.