A Dimer ABC

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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Cited by in corpus (13)

• Almost gentle algebras and their trivial extensions
• Mapping cones in the bounded derived category of a gentle algebra
• Deformations of Dimer Models
• Some Open Questions in Quiver Gauge Theory
• Mutations of splitting maximal modifying modules: The case of reflexive polygons
• Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds
• Consistent Dimer Models on Surfaces with Boundary
• Rigid potentials for cluster algebras from double Bruhat cells
• Calabi-Yau properties of ribbon graph orders
• Strebel Differentials and stable Matrix Factorizations
• Zhegalkin Zebra Motives Digital Recordings of Mirror Symmetry
• Cyclic contractions of dimer algebras always exist
• Semi-steady non-commutative crepant resolutions via regular dimer models