William Fulton works in algebraic geometry. He has three main areas that he will concentrate on during this research program. The first is the subject of Chern classes of direct image bundles for branched coverings of projective spaces. The next is intersection theory and enumerative geometry. This includes the search for Porteous formulae in the presence of singularities or excess components and questions of reality or rationality of solutions. The last is the applications of intersection theory to toric varieties and to varieties of geometric figures such as n-tuples of points. Algebraic geometry is the study of the geometric objects arising from the sets of zeros of systems of polynomial equations. This is one of the oldest and currently one of the most active branches of mathematics with widespread applications through out mathematics and reaching into physics, computer science etc. Fulton is one of the very best practitioners of this subject with his constant flow of very deep contributions. This proposal will undoubtedly lead to many more exciting results.
