Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7
B1, B2, B3, B4, B5, B6, B7
C1, C2, C3, C4, C5
Topology & Equivariant Theories
A7: Derived categories of singular curves
Burban, Marinescu
Abstract:
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.
Group:
 
Prof. Igor Burban (PI)
mail: burban at math.uni-koeln.de
phone: 0221 / 470 3431
room: 106
Mathematical Institute
University of Cologne
Prof. George Marinescu (PI)
mail: gmarines at math.uni-koeln.de
phone: 0221 / 470 2661
room: 112
Mathematical Institute
University of Cologne
Hendrik Herrmann (ds)
mail: heherrma at math.uni-koeln.de
phone: 0221 / 470 1303
room: C107 (Gyrhofstr. 8a)
Mathematical Institute
University of Cologne
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum