The aim of this paper is to introduce τ-tilting theory, which 'completes'(classical) tilting theory
from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting …

The class of support-tilting modules was introduced to provide a completion of the class of
tilting modules from the point of view of mutations. In this article, we study-tilting finite …

We study the affine schemes of modules over gentle algebras. We describe the smooth
points of these schemes, and we also analyze their irreducible components in detail …

Let Y be a (partial) minimal model of a scheme V with a cluster structure (of type A, X or of a
quotient of A or a fibre of X). Under natural assumptions, for every choice of seed we …

The-vector fan of a finite-dimensional algebra is a fan whose rays are the-vectors of its two-
term presilting objects. We prove that the-vector fan of a tame algebra is dense. We then …

In this short note, we state a stable and a $\tau $-reduced version of the second Brauer-
Thrall Conjecture. The former is a slight strengthening of a brick version of the second …

We study semicontinuous maps on varieties of modules over finite-dimensional algebras.
We prove that truncated Euler maps are upper or lower semicontinuous. This implies that 𝑔 …

Let $ K $ be a an algebraically closed field with $\operatorname {char}(K)\neq 2$, and $ A $
a skewed-gentle $ K $-algebra. In this case, Crawley-Boevey's description of the …

For a finite-dimensional simple Lie algebra g admitting a non-trivial minuscule
representation and a connected marked surface Σ with at least two marked points and no …

We study the relation between the integer tropical points of a cluster variety (satisfying the
full Fock-Goncharov conjecture) and the totally positive part of the tropicalization of an ideal …