We introduce a new class of triangulated categories, which are Verdier quotients of three-
Calabi–Yau categories from (decorated) marked surfaces, and show that its spaces of …

We introduce the cluster exchange groupoid associated to a non-degenerate quiver with
potential, as an enhancement of the cluster exchange graph. In the case that arises from an …

Categorically, we introduce the Calabi-Yau-$\mathbb {X} $ categories $\mathcal {D} _
{\mathbb {X}} $ of a graded marked surface $\mathbf {S}^\lambda $, as a $ q $-deformation …

We survey various generalizations of braid groups for quivers with superpotential and focus
on the cluster braid groups, which are introduced in a joint work with King (2018). Our …

This is a survey on two closely related subjects. First, we review the study of topological
structure offinite type'components of spaces of Bridgeland's stability conditions on …

This is a survey on the projectDecorated Marked Surfaces', where we introduce the
decoration $\Delta $ on a marked surfaces $\mathbf {S} $, to study Calabi-Yau-2 (cluster) …