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 purpose of this work is to prove the existence of an algebraic moduli classifying objects
in a given triangulated category. To any dg-category T (over some base ring k), we define a …

Since the first draft of this text, which appeared in 2012 on the arXiv, the theory of higher
Segal spaces has been further developed in various directions by several groups of authors …

To any quiver with relations we associate a consistent scattering diagram taking values in
the motivic Hall algebra of its category of representations. We show that the chamber …

This paper concerns the cohomological aspects of Donaldson–Thomas theory for Jacobi
algebras and the associated cohomological Hall algebra, introduced by Kontsevich and …

These are notes for a minicourse on Hall algebras given at the ICTP in Trieste in January
2006. After giving the definition and first properties of Hall algebras, we study in some details …

We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas
curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants and …

The Donaldson-Thomas invariant is a curve counting invariant on Calabi-Yau 3-folds via
ideal sheaves. Another counting invariant via stable pairs is introduced by Pandharipande …

Enumerative invariants in Algebraic Geometry'count'$\tau $-(semi) stable objects $ E $ with
fixed topological invariants $[E]= a $ in some geometric problem, using a virtual class $[{\cal …

The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas
invariant for a quiver with zero potential and a generic stability condition agrees with the …