The purpose of this project is to develop a comprehensive theory of discrete Riemann surfaces, i.e., to discretize the notions and theorems of complex analysis, and to study related questions in other fields of mathematics. Important problems concern, e.g., discrete uniformization theorems and discrete simultaneous uniformization, ideal and hyperideal polyhdera in hyperbolic space, quasi-fuchsian 3-manifolds with polyhedral boundary, questions of convergence of discrete conformal maps, and geometric interpretations of integrable systems, of discrete models of statistical physics like the dimer model, and of cluster algebra structures.
DFG Programme
CRC/Transregios
