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Journal articles on the topic 'SYZ conjecture'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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1

Martínez, Cristina. "Abelian fibrations and SYZ mirror conjecture." Comptes Rendus Mathematique 350, no. 13-14 (2012): 689–92. http://dx.doi.org/10.1016/j.crma.2012.07.011.

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2

Nye, Logan. "The SYZ Conjecture through Computational Equivalence." Advances in Pure Mathematics 15, no. 02 (2025): 145–81. https://doi.org/10.4236/apm.2025.152007.

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3

Verbitsky, Misha. "Hyperkähler Syz Conjecture and Semipositive Line Bundles." Geometric and Functional Analysis 19, no. 5 (2009): 1481–93. http://dx.doi.org/10.1007/s00039-009-0037-z.

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4

Li, Yang. "Metric SYZ conjecture for certain toric Fano hypersurfaces." Cambridge Journal of Mathematics 12, no. 1 (2024): 223–52. http://dx.doi.org/10.4310/cjm.2024.v12.n1.a3.

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5

Fang, Bohan, Chiu-Chu Melissa Liu, and Zhengyu Zong. "The SYZ mirror symmetry and the BKMP remodeling conjecture." Advances in Theoretical and Mathematical Physics 20, no. 1 (2016): 165–92. http://dx.doi.org/10.4310/atmp.2016.v20.n1.a3.

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6

Joyce, Dominic. "Singularities of special Lagrangian fibrations and the SYZ Conjecture." Communications in Analysis and Geometry 11, no. 5 (2003): 859–907. http://dx.doi.org/10.4310/cag.2003.v11.n5.a3.

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7

Chan, Kwokwai. "A glimpse of the SYZ conjecture and related developments." Notices of the International Congress of Chinese Mathematicians 4, no. 1 (2016): 14–28. http://dx.doi.org/10.4310/iccm.2016.v4.n1.a3.

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8

Sloterdijk, Peter, and Robert Hughes. "To Stir the Sleep of the World: Conjectures on Awakening." symploke 29, no. 1-2 (2021): 301–32. http://dx.doi.org/10.1353/sym.2021.0017.

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9

Yuan, Hang. "Family Floer mirror space for local SYZ singularities." Forum of Mathematics, Sigma 12 (2024). https://doi.org/10.1017/fms.2024.107.

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Abstract We give a mathematically precise statement of the SYZ conjecture between mirror space pairs and prove it for any toric Calabi-Yau manifold with the Gross Lagrangian fibration. To date, it is the first time we realize the SYZ proposal with singular fibers beyond the topological level. The dual singular fibration is explicitly written and proved to be compatible with the family Floer mirror construction. Moreover, we discover that the Maurer-Cartan set of a singular Lagrangian is only a strict subset of the corresponding dual singular fiber. This responds negatively to the previous expe
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10

Li, Yang. "Metric SYZ conjecture and non-Archimedean geometry." Duke Mathematical Journal -1, no. -1 (2023). http://dx.doi.org/10.1215/00127094-2022-0099.

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11

Chan, Kwokwai, Naichung Conan Leung, and Ziming Nikolas Ma. "Smoothing, scattering and a conjecture of fukaya." Forum of Mathematics, Pi 13 (2025). https://doi.org/10.1017/fmp.2024.32.

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Abstract In 2002, Fukaya [19] proposed a remarkable explanation of mirror symmetry detailing the Strominger–Yau–Zaslow (SYZ) conjecture [47] by introducing two correspondences: one between the theory of pseudo-holomorphic curves on a Calabi–Yau manifold $\check {X}$ and the multivalued Morse theory on the base $\check {B}$ of an SYZ fibration $\check {p}\colon \check {X}\to \check {B}$ , and the other between deformation theory of the mirror X and the same multivalued Morse theory on $\check {B}$ . In this paper, we prove a reformulation of the main conjecture in Fukaya’s second correspondence
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12

Li, Yang. "Survey on the metric SYZ conjecture and non-archimedean geometry." International Journal of Modern Physics A, June 10, 2022. http://dx.doi.org/10.1142/s0217751x22300095.

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13

Kanazawa, Atsushi. "Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves." Symmetry, Integrability and Geometry: Methods and Applications, April 11, 2017. http://dx.doi.org/10.3842/sigma.2017.024.

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14

Anderson, Lara B., Mathis Gerdes, James Gray, Sven Krippendorf, Nikhil Raghuram, and Fabian Ruehle. "Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning." Journal of High Energy Physics 2021, no. 5 (2021). http://dx.doi.org/10.1007/jhep05(2021)013.

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Abstract We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In th
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15

Emmerson, Parker Yaohushuason. "Geometry of Phenomenological Velocity: Energy Numbers, Curvature and Fukaya-Type Categories." May 27, 2025. https://doi.org/10.5281/zenodo.15523017.

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Thank you, Yaohushua for letting me continue to distribute these mathematical gesturing forms so interesting. The paper constructs an algebraic–geometric framework around the “phenomenological ve-locity” expression v = pN/D that arose in previous informal work. We introduce (i) theenergy-number field E, (ii) a non-commutative velocity-string algebra V, (iii) a curvature scalarKPV defined from a “PV–Hessian”, and (iv) a curved A∞ category Fukv (M ) obtained from anordinary Fukaya category by multiplication with v. Basic structural results are proved; se
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