Mathematical Sciences: Capacity Theory, Green's Functions, and Intersection Theory

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This awards supports the research of Professor P. Aluffi to work in algebraic geometry. He will work on problems deriving from the study of hypersurface singularities. He hopes to find a new formula for MacPherson's Chern class and to extend result son duality of projective varieties. He hopes to apply some of these results to the study of combinatorial questions on graphs. 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.