This award supports the research in algebraic geometry of Professor Andrew Sommese of the University of Notre Dame. Dr. Sommese's project is to continue his research on hyperplane sections of complex projective manifolds and the projective classification of complex varieties. He will also continue his studies of the zero-dimensional subschemes of smooth complex projective varieties. This is research in the field 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.
