Mathematical Sciences: Abelian Varieties of Low Dimension, Prym Varieties and Fano Threefolds

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This award supports the research of Professor E. Izadi to work in algebraic geometry. She will work on low dimension principally polarized varieties and their moduli spaces using techniques involving theta divisors. Problems to be studied include questions on cycles in Abelian varieties in dimension 4 with rank greater than one. 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.