PIRSA:25110070 Conference Mathematical physics

DOI10.48660/25110070

Conference/School: Holomorphic-topological field theories and representation theory

Williams, H. (2025). Dimer Models and Tropical Lagrangian Coamoebae. Perimeter Institute. https://pirsa.org/25110070

Williams, Harold. Dimer Models and Tropical Lagrangian Coamoebae. Perimeter Institute, Nov. 07, 2025, https://pirsa.org/25110070 

@misc{ pirsa_PIRSA:25110070,
  doi = {10.48660/25110070},
  url = {https://pirsa.org/25110070},
  author = {Williams, Harold},
  keywords = {Mathematical physics},
  language = {en},
  title = {Dimer Models and Tropical Lagrangian Coamoebae},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {nov},
  note = {PIRSA:25110070 see, \url{https://pirsa.org}}
}

Abstract

Dimer models are of interest from many perspectives across geometry, combinatorics, and mathematical physics. In this talk, we explain how one throughline among these perspectives --- the spectral relationship between dimer models in T^2 and line bundles on curves in (C*)^2 --- may be understood as part of a more general mirror relationship between simplicial complexes in T^n and coherent sheaves on (C*)^n. We refer to the complexes arising this way as tropical Lagrangian coamoebae, as from a symplectic point of view they are in a sense dual objects to tropical varieties. This is joint work with Chris Kuo.

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