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

We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed…

We study $3d$ $\mathcal{N}=4$ quiver gauge theories with gauge nodes forming a $D_n$ Dynkin diagram. The class of good $D_n$ Dynkin quivers is completely characterised and the moduli space singularity structure fully determined for all such…

This paper presents some parallel developments in Quiver/Dimer Models, Hypergeometric Systems and Dessins d'Enfants. The setting in which Gelfand, Kapranov and Zelevinsky have formulated the theory of hypergeometric systems, provides also a…

Given a triangulation of a polygon P with n vertices, we associate an ice quiver with potential such that the associated Jacobian algebra has the structure of a Gorenstein tiled K[x]-order L. Then we show that the stable category of the…

We develop a mutation theory for quivers with oriented 2-cycles using a structure called a homotopy, defined as a normal subgroupoid of the quiver's fundamental groupoid. This framework extends Fomin-Zelevinsky mutations of 2-acyclic…

Let $(Q,W)$ be a quiver with a non degenerate potential. We give a new description of the \textbf{c}-vectors of $Q$. We use it to show that, if $Q$ is mutation equivalent to a Dynkin quiver, then the set of positive $\mathbf{c}$-vectors of…

We construct the moduli space of finite dimensional representations of generalized quivers for arbitrary connected complex reductive groups using Geometric Invariant Theory as well as Symplectic reduction methods. We explicit characterize…

In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix representation of these reflections is determined by a linear…

We study the moduli space of twisted quasimaps from a fixed smooth projective curve to a Nakajima's quiver variety and the moduli space of $\delta$-stable framed twisted quiver bundles with moment map relations. We show that they carry…

For a stability condition $\sigma$ on a triangulated category, Dimitrov-Katzarkov introduced the notion of a $\sigma$-exceptional collection. In this paper, we study full $\sigma$-exceptional collections in the derived category of an…

Graphs which generalize the simple or affine Dynkin diagrams are introduced. Each diagram defines a bilinear form on a root system and thus a reflection group. We present some properties of these groups and of their natural "Coxeter…

We show that the mutation class of a finite quiver without oriented cycles is finite if and only is the quiver is either Dynkin, extended Dynkin or has at most two vertices.

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems…

Let $\la$ be a preprojective algebra of simply laced Dynkin type $\Delta$. We study maximal rigid $\la$-modules, their endomorphism algebras and a mutation operation on these modules. This leads to a representation-theoretic construction of…

Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of…

We claim that 3d monopole quivers, theories with product gauge groups interacting through Affleck-Harvey-Witten superpotentials, are a natural setup for the study of spontaneous breaking 3d $\mathcal{N}=2$ supersymmetry. We give evidence of…

In this paper, we study extension groups of determinantal modules over a preprojective algebra using the Auslander-Reiten translation of the quiver associated with it. More precisely, based on the recent work given by Aizenbud and Lapid, we…

We say that an algebra $\Lambda$ over a commutative noetherian ring $R$ is Calabi-Yau of dimension $d$ ($d$-CY) if the shift functor $[d]$ gives a Serre functor on the bounded derived category of the finite length $\Lambda$-modules. We show…

Let $A$ be the path algebra of a quiver of Dynkin type $\mathbb{A}_n$. The module category $\text{mod}\,A$ has a combinatorial model as the category of diagonals in a polygon $S$ with $n+1$ vertices. The recently introduced notion of almost…

We propose an experimental protocol for using cold atoms to create and probe quantum dimer models, thereby exploring the Pauling-Anderson vision of a macroscopic collection of resonating bonds. This process can allow the study of exotic…