Related papers: Dimer models and group actions

Let X(1,3,a) be a crepant resolution of the quotient singularity C^3/G, where G is a diagonal cyclic subgroup of SL(3,\C) acting on C^3 with weights (1,3,a). For each such X(1,3,a), we construct a (Q,W)-configuration of spherical objects in…

We show that for a non-degenerate dimer model, both the first consistency condition of Mozgovoy and Reineke and the properly-orderedness condition of Gulotta are equivalent to a condition on zigzag paths, which goes back to Hanany and Vegh.…

We explicitly construct a $V$-normal crossing Gorenstein canonical model of the relative symmetric products of a local semistable degeneration of surfaces without a triple point by means of toric geometry. Using this model, we calculate the…

For a general class of cones in $\mathbb{R}^3$, we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mean curvature flow with genus strictly decreasing but not to…

Using characters of finite group representations and monodromy of matter curves in F-GUT, we complete partial results in literature by building SO$% _{10}$ models with dihedral $\mathbb{D}_{4}$ discrete symmetry. We first revisit the…

We construct a consistent example of a topological space $Y=X \cup \{\infty\}$ such that: 1) $Y$ is regular. 2) Every $G_\delta$ subset of $Y$ is open. 3) The point $\infty$ is not isolated, but it is not in the closure of any discrete…

Dimer models (also known as brane tilings) are special bipartite graphs on a torus $\mathbb{T}^2$. They encode the structure of the 4d $\mathcal{N} = 1$ worldvolume theories of D3 branes probing toric affine Calabi-Yau singularities.…

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra $A$ and invariants with respect to recollements of the bounded…

A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…

We demonstrate for the first time the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form $\exp(-|n|)$, i.e., a discrete peakon. These discrete analogs of the well-known, continuum peakons…

A class of non-linear sigma models possessing a new symmetry is identified. The same symmetry is also present in Chern-Simons theories. This hints at a possible topological origin for this class of sigma models. The non-linear sigma models…

We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the…

We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action…

In this note, we provide a description of the structure of homomorphisms from a finitely generated group to any torsion-free (3-dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jorgensen-Thurston…

We introduce and investigate multicomplex configurations, a class of projective varieties constructed via specialization of the polarizations of Artinian monomial ideals. Building upon geometric polarization and geometric vertex…

We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the…

For affine toric varieties, the vector space T1 (containing the infinitesimal deformations) will be interpreted via Minkowski summands of cross cuts of the defining polyhedral cone. This result will be applied to study the deformation…

We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We…

We first generalize classical Auslander-Reiten duality for isolated singularities to cover singularities with a one-dimensional singular locus. We then define the notion of CT modules for non-isolated singularities and we show that these…