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Relevant bibliographies by topics / Cluster Donaldson–Thomas theory

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Academic literature on the topic 'Cluster Donaldson–Thomas theory'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Cluster Donaldson–Thomas theory"

1

Nagao, Kentaro. "Donaldson–Thomas theory and cluster algebras." Duke Mathematical Journal 162, no. 7 (2013): 1313–67. http://dx.doi.org/10.1215/00127094-2142753.

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Reading, Nathan. "Scattering Fans." International Mathematics Research Notices 2020, no. 23 (2018): 9640–73. http://dx.doi.org/10.1093/imrn/rny260.

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Abstract Scattering diagrams arose in the context of mirror symmetry, Donaldson–Thomas theory, and integrable systems. We show that a consistent scattering diagram with minimal support cuts the ambient space into a complete fan. A special class of scattering diagrams, the cluster scattering diagrams, is closely related to cluster algebras. We show that the cluster scattering fan associated to an exchange matrix $B$ refines the mutation fan for $B$ (a complete fan that encodes the geometry of mutations of $B$). We conjecture that, when $B$ is $n\times n$ for $n&gt;2$, these two fans coincid

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3

Gholampour, Amin, Artan Sheshmani, and Shing-Tung Yau. "Localized Donaldson-Thomas theory of surfaces." American Journal of Mathematics 142, no. 2 (2020): 405–42. http://dx.doi.org/10.1353/ajm.2020.0011.

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Fasola, Nadir, and Sergej Monavari. "Tetrahedron instantons in Donaldson-Thomas theory." Advances in Mathematics 462 (February 2025): 110099. https://doi.org/10.1016/j.aim.2024.110099.

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5

Maulik, Davesh, та Alexei Oblomkov. "Donaldson–Thomas theory of 𝒜n×P1". Compositio Mathematica 145, № 5 (2009): 1249–76. http://dx.doi.org/10.1112/s0010437x09003972.

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AbstractWe study the relative Donaldson–Thomas theory of 𝒜n×P1, where 𝒜n is the surface resolution of type An singularity. The action of divisor operators in the theory is expressed in terms of operators of the affine algebra $\glh $ on Fock space. Assuming a nondegeneracy conjecture, this gives a complete solution for the theory. The results complete the comparison of this theory with the Gromov–Witten theory of 𝒜n×P1 and the quantum cohomology of the Hilbert scheme of points on 𝒜n.

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Okounkov, Andrei. "Takagi Lectures on Donaldson–Thomas theory." Japanese Journal of Mathematics 14, no. 1 (2019): 67–133. http://dx.doi.org/10.1007/s11537-018-1744-8.

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Maulik, D., N. Nekrasov, A. Okounkov, and R. Pandharipande. "Gromov–Witten theory and Donaldson–Thomas theory, I." Compositio Mathematica 142, no. 05 (2006): 1263–85. http://dx.doi.org/10.1112/s0010437x06002302.

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Maulik, D., N. Nekrasov, A. Okounkov, and R. Pandharipande. "Gromov–Witten theory and Donaldson–Thomas theory, II." Compositio Mathematica 142, no. 05 (2006): 1286–304. http://dx.doi.org/10.1112/s0010437x06002314.

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Kinjo, Tasuki. "Dimensional reduction in cohomological Donaldson–Thomas theory." Compositio Mathematica 158, no. 1 (2022): 123–67. http://dx.doi.org/10.1112/s0010437x21007740.

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For oriented $-1$-shifted symplectic derived Artin stacks, Ben-Bassat, Brav, Bussi and Joyce introduced certain perverse sheaves on them which can be regarded as sheaf-theoretic categorifications of the Donaldson–Thomas invariants. In this paper, we prove that the hypercohomology of the above perverse sheaf on the $-1$-shifted cotangent stack over a quasi-smooth derived Artin stack is isomorphic to the Borel–Moore homology of the base stack up to a certain shift of degree. This is a global version of the dimensional reduction theorem due to Davison. We give two applications of our main theorem

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Cirafici, Michele, Annamaria Sinkovics, and Richard J. Szabo. "Instantons, quivers and noncommutative Donaldson–Thomas theory." Nuclear Physics B 853, no. 2 (2011): 508–605. http://dx.doi.org/10.1016/j.nuclphysb.2011.08.002.

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Dissertations / Theses on the topic "Cluster Donaldson–Thomas theory"

1

Nagao, Kentaro. "Mutations and noncommutative Donaldson-Thomas theory." 名古屋大学多元数理科学研究科, 2009. http://hdl.handle.net/2237/12261.

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2

Bussi, Vittoria. "Derived symplectic structures in generalized Donaldson-Thomas theory and categorification." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:54896cc4-b3fa-4d93-9fa9-2a842ad5e4df.

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This thesis presents a series of results obtained in [13, 18, 19, 23{25, 87]. In [19], we prove a Darboux theorem for derived schemes with symplectic forms of degree k < 0, in the sense of [142]. We use this to show that the classical scheme X = t<sub>0</sub>(X) has the structure of an algebraic d-critical locus, in the sense of Joyce [87]. Then, if (X, s) is an oriented d-critical locus, we prove in [18] that there is a natural perverse sheaf P·<sub>X,s</sub> on X, and in [25], we construct a natural motive MF<sub>X,s</sub>, in a certain quotient ring M<sup>μ</sup><sub>X</sub> of the μ-equiva

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Young, Benjamin. "Counting coloured boxes." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/731.

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This thesis consists of the manuscripts of two research papers. In the first paper, we verify a recent conjecture of Kenyon/Szendroi by computing the generating function for pyramid partitions. Pyramid partitions are closely related to Aztec Diamonds; their generating function turns out to be the partition function for the Donaldson-Thomas theory of a non-commutative resolution of the conifold singularity {x₁x₂ - x₃x₄ = 0}⊂ C⁴. The proof does not require algebraic geometry; it uses a modified version of the domino (or dimer) shuffling algorithm of Elkies, Kuperberg, Larsen and Propp.

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Ranganathan, Dhruv. "Gromov-Witten Theory of Blowups of Toric Threefolds." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/31.

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We use toric symmetry and blowups to study relationships in the Gromov-Witten theories of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$. These two spaces are birationally equivalent via the common blowup space, the permutohedral variety. We prove an equivalence of certain invariants on blowups at only points of $\mathbb{P}^3$ and $\mathbb{P}^1\!\times\!\mathbb{P}^1\!\times\!\mathbb{P}^1$ by showing that these invariants descend from the blowup. Further, the permutohedral variety has nontrivial automorphisms of its cohomology coming from toric symmetry. These sym

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Jagau, Thomas-Christian [Verfasser]. "Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory / Thomas-Christian Jagau." Mainz : Universitätsbibliothek Mainz, 2013. http://d-nb.info/1035840286/34.

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Song, Yinan. "On the Local Donaldson-Thomas theory of curves." Thesis, 2006. http://hdl.handle.net/2429/18570.

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In this thesis, we study the Donaldson-Thomas theory of local curves. The motivation is the Gromov-Witten/Donaldson-Thomas correspondence. First, we review the gauge theory motivation of the original construction and the history of the Donaldson-Thomas theory. Then we review the construction of Gieseker-Maruyama-Simpson moduli spaces and their relation with Hilbert schemes of threefolds. We also review the concept of a perfect obstruction theory and its relation with the virtual fundamental classes. Then we describe the Gromov-Witten/Donaldson-Thomas correspondence and the equivariant generali

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"Donaldson-Thomas theory for Calabi-Yau four-folds." 2013. http://library.cuhk.edu.hk/record=b5549280.

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令X 為個帶有凱勒形式(Kähler form ω) 以及全純四形式( holomorphic four- form Ω )的四維緊致卡拉比丘空間(Calabi-Yau manifolds) 。在一些假設條件下，通過研究Donaldson- Thomas方程所決定的模空間，我們定義了四維Donaldson-Thomas不變量。我們也對四維局部卡拉比丘空間(local Calabi-Yau four-folds) 定義了四維Donaldson-Thomas 不變量，並且將之聯繫到三維Fano空間的Donaldson- Thomas 不變量。在一些情況下，我們還研究了DT/GW不變量對應。最后，我們在模空間光滑時計算了一些四維Donaldson- Thomas不變量。<br>Let X be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kahler form ω and a holomorphic four-form Ω. Under certain assumptions, we de ne Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donal

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Zhou, Zijun. "Relative Orbifold Donaldson-Thomas Theory and the Degeneration Formula." Thesis, 2017. https://doi.org/10.7916/D8PC37RX.

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We generalize the notion of expanded degenerations and pairs for a simple degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We then define stable quotients on the classifying stacks of expanded degenerations and pairs and prove the properness of their moduli’s. On 3-dimensional smooth projective DM stacks this leads to a definition of relative Donaldson-Thomas invariants and the associated degeneration formula.

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Books on the topic "Cluster Donaldson–Thomas theory"

1

Toda, Yukinobu. Recent Progress on the Donaldson–Thomas Theory. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7838-7.

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2

1977-, Song Yinan, ed. A theory of generalized Donaldson-Thomas invariants. American Mathematical Society, 2011.

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3

Toda, Yukinobu. Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8.

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Zhou, Zijun. Relative Orbifold Donaldson-Thomas Theory and the Degeneration Formula. [publisher not identified], 2017.

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5

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. American Mathematical Society, 2012.

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Categorical Donaldson-Thomas Theory for Local Surfaces. Springer, 2024.

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Toda, Yukinobu. Recent Progress on the Donaldson-Thomas Theory: Wall-Crossing and Refined Invariants. Springer Singapore Pte. Limited, 2022.

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Many-body theory of molecules, clusters, and condensed phases. World Scientific, 2010.

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9

String-Math 2015. American Mathematical Society, 2017.

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10

Surveys on Recent Developments in Algebraic Geometry. American Mathematical Society, 2017.

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Book chapters on the topic "Cluster Donaldson–Thomas theory"

1

Kinjo, Tasuki. "An Introduction to Cohomological Donaldson–Thomas Theory." In KIAS Springer Series in Mathematics. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-8249-9_5.

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Toda, Yukinobu. "Categorical DT Theory for Local Surfaces." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_3.

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Toda, Yukinobu. "Categorical Wall-Crossing via Koszul Duality." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_5.

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Toda, Yukinobu. "Window Theorem for DT Categories." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_6.

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Toda, Yukinobu. "D-Critical D/K Equivalence Conjectures." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_4.

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Toda, Yukinobu. "Some Auxiliary Results." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_8.

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Toda, Yukinobu. "Koszul Duality Equivalence." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_2.

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Toda, Yukinobu. "Categorified Hall Products on DT Categories." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_7.

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Toda, Yukinobu. "Introduction." In Categorical Donaldson-Thomas Theory for Local Surfaces. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-61705-8_1.

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Koshevoy, Gleb. "Cluster Decorated Geometric Crystals, Generalized Geometric RSK-Correspondences, and Donaldson-Thomas Transformations." In 2017 MATRIX Annals. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04161-8_25.

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