Dimers and M-curves: Limit shapes from Riemann surfaces.
演讲者
Alexander Bobenko
时间
2026年05月18日 15:30 至 16:30
地点
A7-201
摘要
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.