Mathematical Sciences: Moduli Problems in Algebraic Geometry

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9500964 Thaddeus Professor Thaddeus will study the topology and geometry of quotient varieties using his techniques of flips. In particular he will study configuration spaces of certain projective spaces. He will also study moduli spaces off vector bundles and curves. he hopes to compute relations in their cohomology rings and the associated Hilbert polynomials. 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. ***