Mathematical Sciences: Gaussian Maps and Topology of ComplexSurface Singularities

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This award supports the research of Professor J. Wahl to work in algebraic geometry. He will study the Gaussian map in different situations. Along with his graduate students, he intends to study the stratification of the moduli space of curves of genus g by the corank of the Gaussian map of the canonical bundle. 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.