This award supports the research of Professor D. Jaffe to work in algebraic geometry. He will work on curves and surfaces in complex projective three-space. In particular, he will work on the conjecture that a smooth connected curve, whose degree exceeds its genus by at least four, is not an intersection of two surfaces. 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.
