2-Calabi-Yau范畴中刚体的组合学

有限维Mesh代数的对称性、周期和Calabi-Yau维数

The symmetry, period and Calabi-Yau dimension of finite dimensional mesh algebras

在有限维网格代数类，也称为m-折叠网格代数，我们确定那些是对称的，那些稳定的模范畴是弱卡-丘。我们还给出了，在组合方面，明确的公式期间的任何这样的代数，并为卡拉比-丘弗罗贝纽斯和稳定的卡拉比-丘维，当他们被定义。

具有簇倾斜子范畴的Calabi-Yau范畴的结构

On the structure of Calabi-Yau categories with a cluster tilting subcategory

证明了对于$d \geq 2$，一个赋$d$ -簇倾斜子范畴的代数$d$ -Calabi-Yau三角范畴是一个DG范畴的稳定范畴，该DG范畴完全是$(d+1)$ -Calabi-Yau，并且具有一个非退化的$t$ -结构，其中心具有足够的投射.

2-Calabi-Yau范畴上簇结构的一个非简单的laced版本

A non-simply laced version for cluster structures on 2-Calabi-Yau categories

本文研究了任意域上2-Calabi-Yau或稳定2-Calabi-Yau范畴的非简单形式的簇结构。结果表明，2-Calabi-Yau范畴或稳定的2-Calabi-Yau范畴具有一个既不含圈也不含2-圈的簇倾斜子范畴，它们确实具有广义的簇结构。这特别是在非代数闭域上的簇范畴的情况。

有限型自内射代数的稳定Calabi-Yau维数

Stable Calabi--Yau dimension of self-injective algebras of finite type

利用双模合偶和所谓的稳定内自同构给出了稳定Calabi-Yau维数的一个等价定义.利用它，我们完成了由K. Erdmann，A. Skowroplski，J. Bia \lkowski和A.杜加斯

Relative Calabi-Yau structures

We introduce relative noncommutative Calabi-Yau structures defined on functors of differential graded categories. Examples arise in various contexts such as topology, algebraic geometry, and representation theory. Our main result is a composition law for Calabi-Yau cospans generalizing the classical composition of cobordisms of oriented manifolds. As an application, we construct Calabi-Yau structures on topological Fukaya categories of framed punctured Riemann surfaces.

Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli of objects

We show that a Calabi-Yau structure of dimension $d$ on a smooth dg category $C$ induces a symplectic form of degree $2-d$ on the moduli space of objects $M_{C}$. We show moreover that a relative Calabi-Yau structure on a dg functor $C \to D$ compatible with the absolute Calabi-Yau structure on $C$ induces a Lagrangian structure on the corresponding map of moduli $M_{D} \to M_{C}$.

The interplay between 2-and-3-Calabi--Yau triangulated categories

This short note surveys the constructions of 3-Calabi--Yau triangulated categories with simple-minded collections due to Ginzburg and Kontsevich--Soibelman and the constructions of 2-Calabi--Yau triangulated categories with cluster-tilting objects due to Buan--Marsh--Reineke--Reiten--Todorov and Amiot, and includes a discussion on the normal form of 2-Calabi--Yau triangulated categories with cluster-tilting objects.

Decorated Marked Surfaces: Calabi-Yau categories and related topics

This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration $Δ$ on a marked surfaces $\mathbf{S}$, to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3 (Fukaya) categories, braid groups for quivers with potential, quadratic differentials and stability conditions.

Pre-Calabi-Yau structures and moduli of representations

We establish a system of formal noncommutative calculus for differential forms and polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories. Using an explicit trace map, we show that any $n$-Calabi-Yau structure on a non-positively graded dg algebra $A$ induces a $(2-n)$-shifted symplectic structure on its derived moduli stack of representations; while any $n$-pre-Calabi-Yau structure on $A$ induces a $(2-n)$-shifted Poisson structure on this derived moduli stack.