This awards supports the research of Professor A. Bertram to work in algebraic geometry. He will study the moduli spaces of vector bundles on an algebraic curve. In particular he hopes to derive a rigorous proof of the empirically observed formula of Verlinde and Witten for studying the cohomology groups associated to these moduli spaces. 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.
