Gromov–Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations by Oberdieck, Georg, Pixton, Aaron

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HIGHER GENUS GROMOV–WITTEN THEORY OF $\mathsf{Hilb}^{n}(\mathbb{C}^{2})$ AND $\mathsf{CohFTs}$ ASSOCIATED TO LOCAL CURVES by RAHUL PANDHARIPANDE, HSIAN-HUA TSENG

“…We study the higher genus equivariant Gromov–Witten theory of the Hilbert scheme of $n$ points of $\mathbb{C}^{2}$. …”
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Open Gromov-Witten Invariants from the Augmentation Polynomial by Matthew Mahowald

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Universal Polynomials for Severi Degrees of Toric Surfaces by Federico Ardila, Florian Block

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Relative Node Polynomials for Plane Curves by Florian Block

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Holomorphic anomaly equation for $({\mathbb P}^2,E)$ and the Nekrasov-Shatashvili limit of local ${\mathbb P}^2$ by Pierrick Bousseau, Honglu Fan, Shuai Guo, Longting Wu

“…We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$-insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D.…”
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Virasoro constraints for stable pairs on toric threefolds by Miguel Moreira, Alexei Oblomkov, Andrei Okounkov, Rahul Pandharipande

“…Since the Virasoro constraints in Gromov–Witten theory are known to hold in the toric case, we establish the stationary Virasoro constraints for the theory of stable pairs on toric threefolds. …”
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Gromov Witten Invariants of Blow Ups of P² using Logarithmic Geometry by Lo, Chun Hong

“…We show that Parker’s recursion for computing Gromov-Witten invariants of blow ups of P² can be derived using logarithmic Gromov-Witten theory and punctured maps. We extend the recursion to compute Gromov-Witten invariants with Hodge class insertions.…”
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Quasimaps to GIT fibre bundles and applications by Jeongseok Oh

“…In [4], Brown proved that the I-function of a toric fibration lies on the overruled Lagrangian cone of its $g=0$ Gromov–Witten theory, introduced by Coates and Givental [8]. …”
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Logarithmic Donaldson–Thomas theory by Davesh Maulik, Dhruv Ranganathan

“…Our formalism specializes to the Li–Wu theory of relative ideal sheaves when the divisor is smooth and is parallel to recent work on logarithmic Gromov–Witten theory with expansions.…”
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Cluster decomposition, T-duality, and gerby CFTs by Ando, M, Hellerman, S, Henriques, A, Pantev, T, Sharpe, E

“…We also discuss a number of applications of these results, including predictions for quantum cohomology and Gromov-Witten theory and additional physical understanding of the geometric Langlands program.…”

Extremal Gromov-Witten invariants of the Hilbert scheme of $3$ Points by Jianxun Hu, Zhenbo Qin

“…Li [17, 23], algebraic manipulations related to the Heisenberg operators of Grojnowski [13] and Nakajima [34], and the virtual localization formulas of Gromov-Witten theory [12, 20, 30].…”
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Equivariant quantum connections in positive characteristic by Lee, Jae Hee

“…In this thesis, we apply techniques from symplectic Gromov--Witten theory to study the equivariant quantum connections in positive characteristic. …”
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Virasoro Constraints for Toric Bundles by Tom Coates, Alexander Givental, Hsian-Hua Tseng

“…We show that the Virasoro conjecture in Gromov–Witten theory holds for the the total space of a toric bundle $E \to B$ if and only if it holds for the base B. …”
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Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds by Cao, Yalong, Maulik, Davesh, Toda, Yukinobu

“…In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation of their genus zero invariants using Donaldson–Thomas theory on CY 4-folds. …”
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Skeletons of stable maps II: superabundant geometries by Ranganathan, Dhruv

“…Our approach is to understand the skeleton of a fundamental object in logarithmic Gromov–Witten theory—the stack of prestable maps to the Artin fan. …”
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Zero cycles on the moduli space of curves by Rahul Pandharipande, Johannes Schmitt

“…If C is a nonsingular curve on a nonsingular rational surface of positive degree with respect to the anticanonical class, we prove [C,p_1,...,p_n] is tautological if the number of markings does not exceed the virtual dimension in Gromov-Witten theory of the moduli space of stable maps. …”
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The tautological classes of the moduli spaces of stable maps to flag varieties by Oprea, Dragos Nicolae

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Gopakumar–Vafa invariants via vanishing cycles by Maulik, Davesh, Toda, Yukinobu

“…We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov–Witten theory and Pandharipande–Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. …”
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Conjectures on counting associative 3-folds in $G_2$-manifolds by Joyce, D

“…Several areas of Symplectic Geometry – Gromov–Witten theory, Quantum Cohomology, Lagrangian Floer cohomology, Fukaya categories – are built using ‘counts’ of moduli spaces of J-holomorphic curves in Y , but give an answer depending only on the symplectic manifold (Y,ω), not on the (almost) complex structure J. …”