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pro vyhledávání: '"George, Terrence"'
Autor:
George, Terrence
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, extending the correspondence between dimer models and Harnack curves
Externí odkaz:
http://arxiv.org/abs/2402.07413
Autor:
George, Terrence
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 matrix. Each conductance is expressed as a biratio of Pfaffians as in the
Externí odkaz:
http://arxiv.org/abs/2305.10074
Autor:
Galashin, Pavel, George, Terrence
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 extends the class of minimal graphs on a torus studied by Goncharov-Ken
Externí odkaz:
http://arxiv.org/abs/2212.12962
Autor:
George, Terrence, Ramassamy, Sanjay
Publikováno v:
Comb. Theory, 3(2), 2023
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 local transformations, which form the cluster modular group of the cl
Externí odkaz:
http://arxiv.org/abs/2208.10306
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 inverse map using theta functions on Jacobians of spectral curves. We provid
Externí odkaz:
http://arxiv.org/abs/2207.10146
Autor:
George, Terrence, Inchiostro, Giovanni
Associated to a convex integral polygon $N$ in the plane are two integrable systems: the cluster integrable system of Goncharov and Kenyon constructed from the planar dimer model, and the Beauville integrable system, associated with the toric surface
Externí odkaz:
http://arxiv.org/abs/2207.09528
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 realizations of the cluster integrable systems of Goncharov and Kenyon cons
Externí odkaz:
http://arxiv.org/abs/2108.12692
Cactus networks were introduced by Lam as a generalization of planar electrical networks. He defined a map from these networks to the Grassmannian Gr($n+1,2n$) and showed that the image of this map, $\mathcal X_n$ lies inside the totally nonnegative
Externí odkaz:
http://arxiv.org/abs/2106.15418
Autor:
George, Terrence, Inchiostro, Giovanni
Associated to a convex integral polygon $N$ is a cluster integrable system $\mathcal X_N$ constructed from the dimer model. We compute the group $G_N$ of symmetries of $\mathcal X_N$, called the (2-2) cluster modular group, showing that it is a certa
Externí odkaz:
http://arxiv.org/abs/1909.12896
Autor:
George, Terrence
A biperiodic planar network is a pair $(G,c)$ where $G$ is a graph embedded on the torus and $c$ is a function from the edges of $G$ to non-zero complex numbers. Associated to the discrete Laplacian on a biperiodic planar network is its spectrum: a t
Externí odkaz:
http://arxiv.org/abs/1901.06353