Topology & Equivariant Theories 
A1, A2, A3, A5, A6, A7

Dynamics & Variational Methods 
B1, B2, B3, B4, B5, B6, B7

Algebra, Combinatorics & Optimization 
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, FourierMukai 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. Matrixvalued Szegö kernels "geometrize" the theory of the associative and classical YangBaxter 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.unikoeln.de  phone: 0221 / 470 3431  room: 106  Mathematical Institute  University of Cologne 
  Prof. George Marinescu (PI)  mail: gmarines at math.unikoeln.de  phone: 0221 / 470 2661  room: 112  Mathematical Institute  University of Cologne 
  Hendrik Herrmann (ds)  mail: heherrma at math.unikoeln.de  phone: 0221 / 470 1303  room: C107 (Gyrhofstr. 8a)  Mathematical Institute  University of Cologne 


