Discrete Riemann surfaces (A01)

• Subject Area: Mathematics
• Term: from 2012 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 195170736

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
• Subproject of: TRR 109: Discretisation in Geometry and Dynamics
• Applicant Institution: Technische Universität Berlin
• Project Heads: Professor Dr. Alexander I. Bobenko; Dr. Ulrike Bücking; Professor Dr. Boris Springborn