Mathematical Sciences: Moduli of Vector Bundles on AlgebraicSurfaces

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This awards supports the research of Professor J. Li to work in algebraic geometry. He will study moduli spaces of vector bundles on algebraic surfaces. In particular he will study the Kodaira dimension, the Picard group, the Donaldson polynomial invariants as well as moduli spaces for higher rank bundles. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.