相关论文: Dimer models on cylinders over Dynkin diagrams and…

Inspired by recent work of Cerulli-Feigin-Reineke on desingularizations of quiver Grassmannians of representations of Dynkin quivers, we obtain desingularizations in considerably more general situations and in particular for Grassmannians…

Let $\mathcal{G}$ be a fusion category acting on a triangulated category $\mathcal{D}$, in the sense that $\mathcal{D}$ is a $\mathcal{G}$-module category. Our motivation example is fusion-weighted species, which is essentially Heng's…

We describe the relationship between dimer models on the real two-torus and coamoebas of curves in (\CC^\times)^2. We show, inter alia, that the dimer model obtained from the shell of the coamoeba is a deformation retract of the closed…

The problem of solving non-linear equations would be considerably simplified by a possibility to convert known solutions into the new ones. This could seem an element of art, but in the context of ADHM-like equations describing quiver…

Let Q be a finite quiver without oriented cycles, and let $\Lambda$ be the associated preprojective algebra. To each terminal representation M of Q (these are certain preinjective representations), we attach a natural subcategory $C_M$ of…

In 2010, Everitt and Fountain introduced the concept of reflection monoids. The Boolean reflection monoids form a family of reflection monoids (symmetric inverse semigroups are Boolean reflection monoids of type $A$). In this paper, we give…

In the same way the folding of the Dynkin diagram of A_{2n} (resp. A_{2n-1}) produces the B_n (resp. C_n) Dynkin diagram, the symmetry algebra W of a Toda model based on B_n (resp. C_n) can be seen as resulting from the folding of a…

Supersymmetric models, in most cases, suffer from the lack of non-perturbative techniques. Recently, an approach based on Dyson-Schwinger equations has been proposed for the massless Wess-Zumino model. In this case, the equations for the…

The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $\mathbb{S}^2$-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of…

We investigate $N=2$ supersymmetric sigma model orbifolds of the sphere in the large radius limit. These correspond to $N=2$ superconformal field theories. Using the equations of topological-anti-topological fusion for the topological…

This paper uses previous results of the authors on vector-valued modular forms to study certain non-congruence modular forms. We prove that these forms have unbounded denominators, and in certain cases we verify congruences of…

The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the…

In this paper, we give a complete classification of silted algebras for the quiver $\overrightarrow{\mathbb{A}}_{n}$ of type $\mathbb{A}_{n}$ with linear orientation and for the quiver obtained from $\overrightarrow{\mathbb{A}}_{n}$ by…

Derksen-Weyman-Zelevinsky's mutation theory of finite-dimensional representations of quivers with potential is generalized to the framework of infinite-dimensional modules.

The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can…

In this survey paper we give an overview of a generalization, introduced by R. Bautista and the author, of the theory of mutation of quivers with potential developed in 2007 by Derksen-Weyman-Zelevinsky. This new construction allows us to…

We realize Derksen-Weyman-Zelevinsky's mutations of representations as densely-defined regular maps on representation spaces, and study the generic values of Caldero-Chapoton functions with coefficients, giving, for instance, a sufficient…

We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $\Gamma$, that allow the presence of several moduli and make connection with the theory of automorphic forms.…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

We study a new class of quiver algebras on surfaces, called 'geodesic ghor algebras'. These algebras generalize cancellative dimer algebras on a torus to higher genus surfaces, where the relations come from perfect matchings rather than a…