Mathematical Sciences: Higher Dimensional Algebraic Varieties

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This award supports the research of Professor J. Kollar to work in algebraic geometry. He will work on the geometric approach to minimal models in dimension three. The research is primarily concerned with finding minimal models for singular threefolds in all characteristics. 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.