Project | Paderborn University

Overview

In this project, we shall apply techniques of algebraic geometry and homological algebra (derived categories, Fourier-Mukai transforms, vector bundles on possibly singular Riemann surfaces) to study problems of geometric analysis. In particular, we shall investigate Bochner Laplacians and kernel functions (Bergman and Szeg? kernels) attached to vector bundles on (possibly singular) compact Riemann surfaces. Matrix-valued Szeg? kernels "geometrize" the theory of the associative and classical Yang-Baxter equations. The study of Bochner Laplacians and Bergman kernels attached to line bundles on singular Riemann surfaces or orbifolds should bring new insights in the mathematical theory of the fractional Hall effect.