Related papers: Calabi-Yau categories and graded quivers with pote…

We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a…

We generalise to a group homomorphism $\tau$ the $\chi$-graded categories of S\"{o}zer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure…

We present a novel way to classify Calabi-Yau threefolds by systematically studying their infinite volume limits. Each such limit is at infinite distance in Kahler moduli space and can be classified by an associated limiting mixed Hodge…

In this paper, we investigate Keller's deformed Calabi--Yau completion of the derived category of coherent sheaves on a smooth variety. In particular, for an $n$-dimensional smooth variety $Y$, we describe the derived category of the total…

We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi--Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We show that, in the case where the category is the generalised…

Inspired by the homological mirror symmetry conjecture of Kontsevich, we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth Calabi-Yau variety.

In this work, we establish a categorification of the classical Dold-Kan correspondence in the form of an equivalence between suitably defined $\infty$-categories of simplicial stable $\infty$-categories and connective chain complexes of…

We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary…

In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and the triangulated category of singularities of the fiber of W over zero. The main…

We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.

Any Calabi-Yau threefold X with infinite fundamental group admits an \'etale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. We call X of type A in the former case and of type K in the…

In five- and six-dimensional $U(N)$ and $SU(N)$ gauge theories compactified on $S^1/Z_2$ and $T^2/Z_3$ orbifolds, we propose a new method to classify the equivalence classes (ECs) of boundary conditions (BCs) wihtout depending on the…

We formulate the homotopy associative (A_\infty) category of D-particle field states via gauged S-duality. By invoking the minimal model theorem of this D-particle field category, we investigate the equivalence principle and the A_\infty…

While many different models for $(\infty,1)$-categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for $(\infty,…

Building on work by Geiss-Leclerc-Schroer and by Buan-Iyama-Reiten-Scott we investigate the link between certain cluster algebras with coefficients and suitable 2-Calabi-Yau categories. These include the cluster-categories associated with…

In 2015, Van den Bergh showed that complete 3-Calabi-Yau algebras over an algebraically closed field of characteristic 0 are equivalent to Ginzburg dg algebras associated with quivers with potential. He also proved the natural…

Let $X$ be a normal projective variety admitting a polarized endomorphism $f$, i.e., $f^*H\sim qH$ for some ample divisor $H$ and integer $q>1$. Then Broustet and Gongyo proposed the conjecture that $X$ is of Calabi-Yau type (CY for short),…

This is part of an ongoing program to classify maximal orders on surfaces via their ramification data. Del Pezzo and ruled orders have already been classified. In this paper, we classify numerically Calabi-Yau orders which are the…

EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…

We introduce infinite discrete versions of the symmetric Nakayama representations by using techniques of persistence theory. After stabilising, we obtain a family triangulated categories which can be regarded as negative Calabi-Yau versions…