Mathematical Sciences: Analytic Number Theory, Automorphic Forms, and Application

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This award supports the research in algebraic geometry, coding theory, and analytic number theory of Professor Carlos J. Moreno of Baruch College of the City University of New York. Dr. Moreno will be working on several questions, all inter- disciplinary within mathematics. One of these is to apply techniques of algebraic geometry to the theory of the error correcting codes arising from algebraic curves that were first developed by Goppa. Another field in which Dr. Moreno will be working involves congruence properties for the weight multiplicities and partition functions of highest weight representations of Kac-Moody Lie algebras. The several themes of Professor Moreno's research are unified by his expertise in algebraic geometry. This 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 theoretical computer science and in robotics.