Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
A1, A2, A3, A5, A6, A7, A8
B1, B2, B3, B4, B5, B6, B7, B8
C1, C2, C3, C4, C5, C6, C7
Topology & Equivariant Theories
A7: Derived categories of singular curves
(completed in the first funding period 2017-2020)
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 Szegö kernels) attached to vector bundles on (possibly singular) compact Riemann surfaces. Matrix-valued Szegö 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.
Impressum Institution of DFG, MI University of Cologne, FM Ruhr-University Bochum and MI University of Heidelberg