TL;DR
This paper reviews recent advances in dimer models, exploring their connections to mirror symmetry, dynamical systems, singularity resolutions, and the unifying role of clusters and categories.
Contribution
It provides a comprehensive overview linking dimer models to mirror symmetry, dynamical systems, and singularity theory, highlighting new interdisciplinary connections.
Findings
Dimer models relate to mirror symmetry in physics and mathematics.
Connections between dimers, cluster algebras, and stability conditions are explored.
The paper proposes a broader framework unifying these topics.
Abstract
We give an overview of recent developments in the theory of dimer models. The viewpoint we take is inspired by mirror symmetry. After an introduction to the combinatorics of dimer models, we will first look at dimers in dynamical systems and statistical mechanics, which can be viewed as coming from the A-model in mirror symmetry. Then we will discuss the role of dimers in the theory of resolutions of singularities, which is inspired by the B-model. The C stands for the connections that tie both subjects together: clusters, categories, and stability conditions. In this final part we will give some ideas on how these two stories fit in a broader framework.
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