The Zoo of Discrete Conformal Structures
Explore the diverse landscape of discrete conformal structures in this Fields Institute lecture from the Workshop on the Geometry of Circle Packings. Delve into David Glickenstein's comprehensive analysis of Thurston's circle packing formulation and Luo's multiplicative edge weight approach. Examine key properties, convergence of discrete conformal mappings, and the formation of geometric structures on Poincaré duals. Investigate the classification of discrete conformal structures and their relationship to curvature variations and discrete Laplacians. Learn about applications to discrete conformal mapping problems and recent rigidity results. Gain insights into hyperbolic backgrounds, dual structures, and potential future directions in this field of geometric analysis.