Related papers: Reconstruction theorems for genus 2 Gromov-Witten …

We explore the theory of connected Gromov-Witten invariants of the symmetric product stack [Sym^n(A_r)]. We derive closed-form expressions for all equivariant invariants with two insertions and reveal a natural correspondence between the…

We determine the all-genus Hodge-Gromov-Witten theory of a smooth hypersurface in weighted projective space defined by a chain or loop polynomial. In particular, we obtain the first genus-zero computation of Gromov-Witten invariants for…

We prove that the system of Gromov-Witten invariants of the product of two varieties is equal to the tensor product of the systems of Gromov-Witten invariants of the two factors.

For a gerbe $\Y$ over a smooth proper Deligne-Mumford stack $\B$ banded by a finite group $G$, we prove a structure result on the Gromov-Witten theory of $\Y$, expressing Gromov-Witten invariants of $\Y$ in terms of Gromov-Witten invariants…

Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov--Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and…

A conjecture of Aganagic and Vafa relates the open Gromov-Witten theory of $X=\mathcal{O}_{\mathbb{P}^{1}}(-1,-1)$ to the augmentation polynomial of Legendrian contact homology. We describe how to use this conjecture to compute genus zero,…

Pandharipande-Pixton-Zvonkine's proof of Pixton's generalized Faber-Zagier relations in the tautological ring of $\overline M_{g, n}$ has started the study of tautological relations from semisimple cohomological field theories. In this…

Motivated by the real version of the Gopakumar-Vafa conjecture for 3-folds, the authors introduced in [GI] the notion of local real Gromov-Witten invariants associated to local 3-folds over Real curves. This article is devoted to the proof…

We first study the quantum product on the big phase space defined by gravitational Gromov-Witten invariants. We then use this product to give an interpretation for various topological recursion relations and also use it to study the…

A. Zinger defined reduced Gromov-Witten (GW) invariants and proved a comparison theorem of standard and reduced genus one GW invariants for every symplectic manifold (with all dimension). H. -L. Chang and J. Li provided a proof of the…

We compute local Gromov-Witten invariants of cubic surfaces at all genera. We use a deformation of a cubic surface to a nef toric surface and the deformation invariance of Gromov-Witten invariants.

We introduce twisted K-theoretic Gromov-Witten invariants - in the frameworks of both "ordinary" and permutation-equivariant K-theoretic GW theory defined recently by Givental. We focus on the case when the twisting is given by the Euler…

Given a closed symplectic manifold $X$, we construct Gromov-Witten-type invariants valued both in (complex) $K$-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is $K_p(n)$-local for some Morava $K$-theory $K_p(n)$.…

We prove a formula of Dale Peterson comparing genus zero Gromov-Witten invariants of $G/P$ to those of $G/B$ using results of Atiyah-Bott and Ramanathan on canonical reductions of principal bundles.

We prove a $q$-refined correspondence theorem between higher genus relative Gromov-Witten invariants with a Lambda class $\lambda_{g-g'}$ insertion in the blow-up of $\mathbb{P}^2$ at $k$ points on a conic and the refined counts of genus…

We construct a fully equivariant correspondence between Gromov-Witten and stable pairs descendent theories for toric 3-folds X. Our method uses geometric constraints on descendents, A_n surfaces, and the topological vertex. The rationality…

Let X=G/P be a homogeneous space and e_k be the class of a simple coroot in H_2(X). A theorem of Strickland shows that for almost all X, the variety of pointed lines of degree e_k, denoted Z_k(X), is again a homogeneous space. For these X…

We establish a genus zero correspondence between the equivariant Gromov-Witten theory of the Deligne-Mumford stack $[\mathbb{C}^N/G]$ and its blowup at the origin. The relationship generalizes the crepant transformation conjecture of…

We make precise conjectures relating the genus zero Gromov-Witten theory of a nonabelian GIT quotient X//G to that of the associated abelian quotient X//T by a maximal torus T in G.These conjectures imply in particular closed formulas for…

We study the equivariant Gromov-Witten and Donaldson-Thomas theories of $\mathbf{P}^2$-bundles over curves. We show the equivariant GW/DT correspondence holds to first order for certain curve classes