Mathematical Sciences: Curves on Special Surfaces and The Local Miyaoka-Yau Inequality

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This award supports the research of Professor J. Wahl to work in algebraic geometry. One of the problems that Professor Wahl will address will be studying Gaussian maps on K3 surfaces or more generally on possibly singular surfaces with trivial canonical bundle. He will also continue to study topological properties of local singularities. This research uses the techniques of algebraic geometry, 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 physics, theoretical computer science, and robotics.