Project Details
Projekt
Derived categories of singular curves (A07)
Subject Area
Mathematics
Term
from 2017 to 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066
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.
DFG Programme
CRC/Transregios
Applicant Institution
Universität zu Köln
Project Heads
Professor Dr. Igor Burban; Professor Dr. George Teodor Marinescu
