Related papers: Zero dimensional Donaldson-Thomas invariants of th…

In this paper we calculate the motivic Donaldson-Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model programme. We translate this geometric situation into the machinery developed by Kontsevich…

We compute the motivic Donaldson-Thomas theory of small crepant resolutions of toric Calabi-Yau 3-folds.

We show that the fundamental groups of smooth $4$-manifolds that admit geometric decompositions in the sense of Thurston have asymptotic dimension at most four, and equal to 4 when aspherical. We also show that closed $3$-manifold groups…

Let $X$ and $X'$ be nonsingular projective $3$-folds related by a flop of a disjoint union of $(-2)$-curves. We prove a flop formula relating the Donaldson-Thomas invariants of $X$ to those of $X'$, which implies some simple relations among…

In analogy with the Gopakumar-Vafa (GV) conjecture on Calabi-Yau (CY) 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau 4-folds using Gromov-Witten theory and conjectured their integrality. In a joint work with…

For each integer $N\geq 2$, Mari\~no and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invariants. Subsequently, Kronheimer gave a rigorous definition…

In this note, we generalise a result of Lalonde, McDuff and Polterovich concerning the $ C^0 $ flux conjecture, thus confirming the conjecture in new cases of a symplectic manifold. Also, we prove the continuity of the flux homomorphism on…

We solve the part of the Donaldson-Thomas theory of Calabi-Yau threefolds which comes from super-rigid rational curves. As an application, we prove a version of the conjectural Gromov-Witten/Donaldson-Thomas correspondence for contributions…

We discuss the GW/DT correspondence for 3-folds in both the absolute and relative cases. Descendents in Gromov-Witten theory are conjectured to be equivalent to Chern characters of the universal sheaf in Donaldson-Thomas theory. Relative…

Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang-Mills gauge theory from twisting by the Picard group of a four manifold in…

Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a certain six-dimensional cohomological gauge theory. We introduce a certain class of defects in this gauge theory which generalize surface defects in four dimensions.…

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…

We present several expected properties of the holomorphic Floer theory of a holomorphic symplectic manifold. In particular, we propose a conjecture relating holomorphic Floer theory of Hitchin integrable systems and Donaldson-Thomas…

Given a complex 4-fold $X$ with an (Calabi-Yau 3-fold) anti-canonical divisor $Y$, we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-Thomas cohomologies of $Y$. We also discuss gluing formulas…

We formulate a theory of pointed manifolds, accommodating both embeddings and Pontryagin-Thom collapse maps, so as to present a common generalization of Poincar\'e duality in topology and Koszul duality in $\mathcal{E}_n$-algebra.

We show the existence of semiorthogonal decompositions (SOD) of Pandharipande-Thomas (PT) stable pair moduli spaces on Calabi-Yau 3-folds with irreducible curve classes, assuming relevant moduli spaces are non-singular. The above result is…

We prove the period-index conjecture for unramified Brauer classes on abelian threefolds. To do so, we develop a theory of reduced Donaldson-Thomas invariants for 3-dimensional Calabi-Yau categories, with the feature that the noncommutative…

We prove wall-crossing formula for categorical Donaldson-Thomas invariants on the resolved conifold, which categorifies Nagao-Nakajima wall-crossing formula for numerical DT invariants on it. The categorified Hall products are used to…

We show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are proper algebraic stacks of finite type, if they satisfy the Bogomolov-Gieseker (BG for short) inequality conjecture proposed by Bayer, Macr\`i…

We determine the structure of certain moduli spaces of ideal sheaves by generalizing an earlier result of the first author. As applications, we compute the (virtual) Hodge polynomials of these moduli space, and calculate the…