Szenes 9870053 The project is concerned with topological invariants of special spaces arising both in algebraic geometry and quantum physics: the moduli spaces of parabolic vector bundles over Riemann surfaces. A detailed geometric analysis of the intersection numbers of these moduli spaces will be pursued by relating them to certain problems of the theory of hyperplane arrangements. A new algebro-geometric model of topological quantum field theories will be studied and relations with deformation quantization will be explored. 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, partly due to some recently discovered surprizing connections with quantum physics. 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.
