Limit shapes and harmonic tricks
Abstract.
The talk will be on the tangent plane method — a novel method for analysis of limit shapes of the dimer model. It will consist of three parts. In the first part, we will briefly introduce the dimer model and the necessary concepts including the associated variational problem. The second part will focus on the underlying geometry using harmonic parametrization. In the third part, we will consider two specific examples of limit shape parametrized by a modular parameter: the Aztec diamond with a hole, and a hexagon with a hexagonal hole. The talk is based on arXiv:2603.21255 (https://arxiv.org/abs/2603.21255).