By Auslander's algebraic McKay correspondence, the stable category of Cohen-Macaulay
modules over a simple singularity is triangle equivalent to the $1 $-cluster category of the …

In a survey paper in 2011, Amiot proposed a conjectural characterisation of the cluster
categories which were conceived in the mid 2000s to lift the combinatorics of Fomin …

We build foundations of an approach to study canonical forms of $2 $-Calabi--Yau
triangulated categories with cluster-tilting objects, using dg algebras and relative singularity …

Proceedings of the International Congress of Mathematicians (ICM 2018) : TILTING COHEN–MACAULAY
REPRESENTATIONS Page 1 P . I . C . M . – 2018 Rio de Janeiro, Vol. 2 (125–162) TILTING …

We study the relationship between singularity categories and relative singularity categories
and discuss constructions of differential graded algebras of relative singularity categories …

Given a negatively graded Calabi-Yau algebra, we regard it as a DG algebra with vanishing
differentials and study its cluster category. We show that this DG algebra is sign-twisted …

Given a noncommutative partial resolution A= End R (R⊕ M) of a Gorenstein singularity R,
we show that the relative singularity category Δ R (A) of Kalck–Yang is controlled by a …

We construct Kn\" orrer type equivalences outside of the hypersurface case, namely,
between singularity categories of cyclic quotient surface singularities and certain finite …

A version of the Bondal-Orlov conjecture, proved by Bridgeland, states that if $ X $ and $ Y $
are smooth complex projective threefolds linked by a flop, then they are derived equivalent …

We give a structure theorem for Calabi-Yau triangulated category with a hereditary cluster
tilting object. We prove that an algebraic d-Calabi-Yau triangulated category with a d-cluster …