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
Superdiffusion, Subdiffusion, Integrability - Sarang GopalakrishnanKavli Institute for Theoretical Physics via YouTube The Computational Theory of Riemann-Hilbert Problems - Lecture 4
International Centre for Theoretical Sciences via YouTube Forced Integrable Systems - The Case of Sine-Gordon Equation by Vasudeva Murthy
International Centre for Theoretical Sciences via YouTube Basic Lectures on Bethe Ansatz - Pedagogical Lecture 2
International Centre for Theoretical Sciences via YouTube Finite-Size Effects in Integrable Systems - Lecture 3
International Centre for Theoretical Sciences via YouTube