Current theme: Integrable systems
Mathematics
Orthodiagonal maps, tilings of rectangles and their convergence to the Riemann map
byDavid Pechersky
Abstract:Discrete complex analysis is the study of discrete holomorphic functions. These are functions defined on graphs embedded in the plane that satisfy some discrete analogue of the Cauchy-Riemann equations. While the subject is classical, it has seen a resurgence in the past 20-30 years with the work of Kenyon, Mercat, Smirnov, and many others demonstrating the power of discrete complex analysis as a tool for understanding 2D statistical physics at criticality.
In this talk, we’ll discuss how discrete complex analysis can be applied to solve a purely deterministic problem for a very general class of discretizations of 2D space accommodating a notion of discrete complex analysis.