Dimers and M-curves: Limit Shapes from Riemann Surfaces
Offered By: Institute for Pure & Applied Mathematics (IPAM) via YouTube
Course Description
Overview
Explore a comprehensive lecture on dimer models and M-curves presented by Alexander Bobenko from Technische Universität Berlin at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into a general approach to dimer models analogous to Krichever's scheme in integrable systems theory, leading to models on doubly periodic bipartite graphs with quasiperiodic positive weights. Discover how this generalization from Harnack curves to M-curves reveals transparent algebro-geometric structures, with the Ronkin function and surface tension expressed as integrals of meromorphic differentials. Examine explicit representations for limit shapes in terms of Abelian integrals, and understand the connection to discrete conformal mappings and hyperbolic polyhedra. Learn about the application of Schottky uniformization of Riemann surfaces in computing weights and dimer configurations, with computational results aligning with theoretical predictions.
Syllabus
Alexander Bobenko - Dimers and M-curves: Limit shapes from Riemann surfaces - IPAM at UCLA
Taught by
Institute for Pure & Applied Mathematics (IPAM)
Related Courses
Statistical Mechanics: Algorithms and ComputationsÉcole normale supérieure via Coursera Physics of Materials
Indian Institute of Technology Madras via Swayam From Atoms to Materials: Predictive Theory and Simulations
Purdue University via edX Statistical Mechanics
Indian Institute of Technology Madras via Swayam Thermodynamics: Classical To Statistical
Indian Institute of Technology Guwahati via Swayam