Mathematical Sciences: Studies in Algebraic Geometry

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This awards supports the research of Professor I. Dolgachev to work in algebraic geometry. Professor Dolgachev will study relations between invariants and vector bundles. He also intends to study problems related to instantons and moduli spaces of vector bundles. This 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.