To each triangulation of any surface with marked points on the boundary and orbifold points
of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is …

The smallest set of vertices needed to differentiate or categorize every other vertex in a
graph is referred to as the graph's metric dimension. Finding the class of graphs for a …

Let $\mathcal {D} $ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a
rigid object $ R $. Let $\Lambda=\operatorname {End} _ {\mathcal {D}} R $ be the …

Gentle algebras form a class of finite-dimensional algebras introduced by I. Assem and A.
Skowroński in the 1980s. Modules over such an algebra can be described by string and …

We categorify a class of skew-symmetrizable cluster algebras associated to orbifolds using
locally free representations of the gentle algebras arising from orbifold triangulations. Along …

We consider certain generalizations of gentle algebras that we call semilinear locally gentle
algebras. These rings are examples of semilinear clannish algebras as introduced by the …

We investigate $\tau $-tilting graphs of algebras and their quotient algebras, and obtain a
sufficient condition for the connectivity of $\tau $-tilting graphs to be maintained in quotient …

We give a geometric model for any length heart in the derived category of a gentle algebra,
which is equivalent to the module category of some gentle algebra. To do this, we deform …

The geometric models for the module category and derived category of any gentle algebra
were introduced to realize the objects in module category and derived category by …

Generalized associahedra were introduced by Fomin and Zelevinsky in connection to
cluster algebras of finite type. Ceballos and Pilaud [CP16] showed that all type BCD …