BIMSA > Integrable systems blackboard seminar Integrable systems blackboard seminar Dimers and M-curves: Limit shapes from Riemann surfaces.
Dimers and M-curves: Limit shapes from Riemann surfaces.
Organizers
Andrii Liashyk , Nicolai Reshetikhin , Ruijie Xu
Speaker
Alexander Bobenko
Time
Monday, May 18, 2026 3:30 PM - 4:30 PM
Venue
A7-201
Abstract
We develop a general approach to solution of the inverse problem for dimer models, in particular explicit description of limit shapes for the Aztec diamond. This leads to dimer models on doubly periodic bipartite graphs with quasiperiodic positive weights. Dimer models with periodic weights and their algebro-geometric description by Kenyon and Okounkov via Harnack curves are recovered as a special case. This generalization from Harnack curves to general M-curves, which are in the focus of our approach, leads to transparent algebro-geometric structures. In particular, using variational descriptions, explicit representations for limit shapes are obtained in terms of Abelian integrals. Based on Schottky uniformization of Riemann surfaces, we compute the weights and dimer configurations. The computational results are in complete agreement with the theoretical predictions. The talk is based on joint works with N. Bobenko and Yu. Suris.