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 …

We use τ-tilting theory to give a description of the wall and chamber structure of a finite-
dimensional algebra. We also study D-generic paths in the wall and chamber structure of an …

Inspired by recent work of Geiss–Leclerc–Schröer, we use Hom-finite cluster categories to
give a good candidate set for a basis of (upper) cluster algebras with coefficients arising …

For an arbitrary finite dimensional algebra Λ, we prove that any wide subcategory of modΛ
satisfying a certain finiteness condition is θ-semistable for some stability condition θ. More …

We define a new lattice structure (W,⪯) on the elements of a finite Coxeter group W. This
lattice, called the shard intersection order, is weaker than the weak order and has the …

For any finite dimensional basic associative algebra, we study the presentation spaces and
their relation with the representation spaces. We prove two theorems about a general …

We describe the upper seminormal crystal structure for the $\mu $-supported $\delta $-
vectors for any quiver with potential with reachable frozen vertices, or equivalently for the …

Maximal green sequences appear in the study of Fomin–Zelevinsky's cluster algebras. They
are useful for computing refined Donaldson–-Thomas invariants, constructing twist …

We introduce signed exceptional sequences as factorizations of morphisms in the cluster
morphism category. The objects of this category are wide subcategories of the module …

Given a finite dimensional algebra A over an algebraically closed field, we consider the c-
vectors such as defined by Fu in [18] and we give a new proof of its sign-coherence …