9504297 Daskalopoulos The proposed research lies in the general area of mathematical physics; more specifically, gauge theory. The investigator seeks to gain a better understanding of moduli spaces of vector bundles arising as spaces of solutions to certain problems in theoretical physics and algebraic geometry. Analytic methods such as CR-manifold techniques are to be used to investigate these moduli spaces and their invariants. It is possible that the proposed research will shed light on the relationship between Donaldson and Seiberg-Witten theories. In recent years several unexpected connections between theoretical physics (quantum field theories) and various parts of mathematics (differential topology, and algebraic and differential geometry) have been discovered. Gauge theory began as an attempt to give a unified theoretical framework for describing the four basic forces of nature, and has found many surprising applications in pure mathematics.
