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 …

For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs
(C, D) where C⊂ X is an embedded curve and D⊂ C is a divisor. A virtual class is …

We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on
Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and …

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 …

We give a universal approach to the deformation-obstruction theory of objects of the derived
category of coherent sheaves over a smooth projective family. We recover and generalise …

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 …

A key question in the study of\(\mathcal {N}= 2\) supersymmetric string or field theories is to
understand the decay of BPS bound states across walls of marginal stability in the space of …

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 …