The links between the theory of cluster algebras [19],[20],[6],[22] and functional identities for
the Rogers dilogarithm first became apparent through Fomin-Zelevinsky's proof [21] of …

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure.
Intuitively, they count the number of semistable objects with fixed class in the K-theory of the …

Abstract Donaldson–Thomas invariants $ DT^\alpha (\tau) $ are integers which 'count'$\tau
$-stable coherent sheaves with Chern character $\alpha $ on a Calabi–Yau 3-fold $ X …

The cluster category associated with a finite-dimensional hereditary algebra was introduced
in [21](and in [26] for the An case). It serves in the representation-theoretic approach to …

We continue the study of quivers with potentials and their representations initiated in the first
paper of the series. Here we develop some applications of this theory to cluster algebras. As …

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on
compact Riemann surfaces can be identified with spaces of stability conditions on a class of …

Bijective correspondences are established between (1) silting objects,(2) simple-minded
collections,(3) bounded t-structures with length heart and (4) bounded co-t-structures. These …

We define and investigate deformed n-Calabi–Yau completions of homologically smooth
differential graded (= dg) categories. Important examples are: deformed preprojective …

We show that Derksen–Weyman–Zelevinsky's mutations of quivers with potential yield
equivalences of suitable 3-Calabi–Yau triangulated categories. Our approach is related to …

This book is an introduction to the representation theory of quivers and finite dimensional
algebras. It gives a thorough and modern treatment of the algebraic approach based on …