Dimer Models and Tropical Lagrangian Coamoebae

          @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.