Related papers: Counting invariant of perverse coherent sheaves an…

Let X be a Calabi-Yau 3-fold, T=D^b(coh(X)) the derived category of coherent sheaves on X, and Stab(T) the complex manifold of Bridgeland stability conditions Z on T. It is conjectured that one can define rational numbers J^a(Z) for Z in…

We introduce geometric structures on the space of stability conditions of a three-dimensional Calabi-Yau category which encode the Donaldson-Thomas invariants of the category. We explain in detail a close analogy between these structures,…

This is a survey article on Hall algebras and their applications to the study of motivic invariants of moduli spaces of coherent sheaves on Calabi-Yau threefolds. It is a write-up of my talks at the 2015 Salt Lake City AMS Summer Research…

We present a construction of Donaldson-Thomas invariants for three-dimensional projective Calabi-Yau Deligne-Mumford stacks. We also study the structure of these invariants for etale gerbes over such stacks.

We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694,…

For $g,n\geq 0$ a 3-dimensional Calabi-Yau $A_\infty$-category $\mathcal C_{g,n}$ is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Stab}(\mathcal C_{g,n})$, is a moduli space of quadratic…

Given a quiver with potential associated to a toric Calabi-Yau threefold, the numerical Donaldson-Thomas invariants for the moduli space of framed representations can be computed by using toric localization, which reduces the problem to the…

This work develops new ideas and tools to establish wall-crossing in Calabi-Yau four categories as originally conjectured by Gross-Joyce-Tanaka. In the process, I set up some necessary new language, including a natural refinement of Joyce's…

We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…

This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up of a projective surface at a point. The followings are main results of this…

We study certain DT invariants arising from stable coherent sheaves in a nonsingular projective threefold supported on the members of a linear system of a fixed line bundle. When the canonical bundle of the threefold satisfies certain…

This paper is motivated by the question of how motivic Donaldson--Thomas invariants behave in families. We compute the invariants for some simple families of noncommutative Calabi--Yau threefolds, defined by quivers with homogeneous…

We construct and study Donaldson-Thomas invariants counting orthogonal and symplectic objects in linear categories, which are a generalization of the usual Donaldson-Thomas invariants from the structure groups $\mathrm{GL} (n)$ to the…

We study the reduced Donaldson-Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson-Thomas invariants under all derived autoequivalences, up to explicitly…

Let $Y$ be a smooth projective threefold and let $f:Y\to X$ be a birational map with $Rf_*\mathcal{O}_Y=\mathcal{O}_X$. When $Y$ is Calabi-Yau, Bryan-Steinberg defined enumerative invariants associated to such maps called $f$-relative…

This review gives an introduction to cohomological Donaldson-Thomas theory: the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their numerical DT…

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$,…

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 category ("number of BPS states with given charge" in…

This paper contains some applications of Bridgeland-Douglas stability conditions on triangulated categories, and Joyce's work on counting invariants of semistable objects, to the study of birational geometry. We introduce the notion of…

The invariants of rank 2 Joyce-Song semistable pairs over a Calabi-Yau threefold were computed in arXiv:1101.2252, using the wall-crossing formula of Joyce-Song and Kontsevich-Soibelman. Such wall-crossing computations often depend on the…