Professor Debarre will investigate geometric properties of abelian varieties. In particular, he will study the topology and geometry of covers of abelian varieties of small degree. He also intends to continue his study of the Schottky problem. This is research in the field of algebraic geometry. Algebraic geometry is 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.
