9500938 Tong Professor Tong will study problems that derive from the deeper study of intersection theory and moduli spaces. He hopes to study more algebraically the flat projective connections on certain vector bundles over Teichmuller space. He also wishes to study the connections between the BRST differential studied in mathematical physics and the Cech-Koszul complex. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. Algebraic geometry itself is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics. ***
