4 citations · 14 across the 12 of their papers we have counts for
14 papers
Tropicalization of Fock's inverse spectral transform
Terrence George
The dimer spectral transform gives algebro-geometric action-angle coordinates for cluster integrable systems. Fock gave an explicit formula for its inverse. We study Fock's inverse…
Dimer models on astroidal zig-zag graphs
Tomas Berggren, Alexei Borodin, Terrence George
On a finite weighted graph, the dimer model is a probability measure on its dimer covers, that assigns to any cover a probability proportional to the product of the weights of its…
Multiple cluster algebra structures for TCD maps I: theoretical framework
Niklas Affolter, Terrence George, Max Glick +1
We introduce triple crossing diagram (TCD) maps, which encode projective configurations of points and lines, as a unified framework for constructions arising in various areas of ge…
Spectral transform for the Ising model
Terrence George
We prove a correspondence between Ising models in a torus and the algebro-geometric data of a Harnack curve with a certain symmetry and a point in the real part of its Prym variety…
The twist for electrical networks and the inverse problem
Terrence George
We construct an electrical-network version of the twist map for the positive Grassmannian, and use it to solve the inverse problem of recovering conductances from the response matr…
Move-reduced graphs on a torus
Pavel Galashin, Terrence George
We determine which bipartite graphs embedded in a torus are move-reduced. In addition, we classify equivalence classes of such move-reduced graphs under square/spider moves. This e…
Discrete dynamics in cluster integrable systems from geometric -matrix transformations
Terrence George, Sanjay Ramassamy
Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of…
The inverse spectral map for dimers
Terrence George, Alexander Goncharov, Richard Kenyon
In 2015, Vladimir Fock proved that the spectral transform, associating to an element of a dimer cluster integrable system its spectral data, is birational by constructing an invers…
Dimers and Beauville integrable systems
Terrence George, Giovanni Inchiostro
Associated to a convex integral polygon in the plane are two integrable systems: the cluster integrable system of Goncharov and Kenyon, constructed from the dimer model on bipa…
Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder
Niklas Christoph Affolter, Terrence George, Sanjay Ramassamy
We introduce twisted triple crossing diagram maps, collections of points in projective space associated to bipartite graphs on the cylinder, and use them to provide geometric reali…
Electrical networks and Lagrangian Grassmannians
Sunita Chepuri, Terrence George, David E Speyer
Cactus networks were introduced by Lam as a generalization of planar electrical networks. He defined a map from these networks to the Grassmannian Gr() and showed that the…
The cluster modular group of the dimer model
Terrence George, Giovanni Inchiostro
Associated to a convex integral polygon is a cluster integrable system constructed from the dimer model. We compute the group of symmetries of $\mathcal X_…
Spectra of biperiodic planar networks
Terrence George
A biperiodic planar network is a pair where is a graph embedded on the torus and is a function from the edges of to non-zero complex numbers. Associated to the…
Grove arctic curves from periodic cluster modular transformations
Terrence George
Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a…