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Journal articles on the topic 'Homological mirror symmetry'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

KONISHI, EIJI. "PLANAR HOMOLOGICAL MIRROR SYMMETRY." International Journal of Modern Physics A 22, no. 29 (2007): 5351–68. http://dx.doi.org/10.1142/s0217751x07037202.

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In this paper, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern–Simons-type topological open string field theory using homotopy associative algebra (A∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT duality of Dijkgraaf–Vafa theory.

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2

Abouzaid, Mohammed. "Homological mirror symmetry without correction." Journal of the American Mathematical Society 34, no. 4 (2021): 1059–173. http://dx.doi.org/10.1090/jams/973.

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Let X X be a closed symplectic manifold equipped with a Lagrangian torus fibration over a base Q Q . A construction first considered by Kontsevich and Soibelman produces from this data a rigid analytic space Y Y , which can be considered as a variant of the T T -dual introduced by Strominger, Yau, and Zaslow. We prove that the Fukaya category of tautologically unobstructed graded Lagrangians in X X embeds fully faithfully in the derived category of (twisted) coherent sheaves on Y Y , under the technical assumption that π 2 ( Q ) \pi _2(Q) vanishes (all known examples satisfy this assumption).

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3

Sato, Matsuo. "Moduli Space in Homological Mirror Symmetry." Advances in Mathematical Physics 2019 (April 30, 2019): 1–11. http://dx.doi.org/10.1155/2019/1693102.

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We prove that the moduli space of the pseudo holomorphic curves in the A-model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B-model on the corresponding elliptic curve. These moduli spaces determine the A∞ structure of the both models.

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4

Katzarkov, L., and V. Przyjalkowski. "Generalized Homological Mirror Symmetry and cubics." Proceedings of the Steklov Institute of Mathematics 264, no. 1 (2009): 87–95. http://dx.doi.org/10.1134/s0081543809010118.

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5

Abouzaid, Mohammed, Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov, and Dmitri Orlov. "Homological mirror symmetry for punctured spheres." Journal of the American Mathematical Society 26, no. 4 (2013): 1051–83. http://dx.doi.org/10.1090/s0894-0347-2013-00770-5.

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6

Zhou, Jian. "Homological Perturbation Theory and Mirror Symmetry." Acta Mathematica Sinica, English Series 19, no. 4 (2003): 695–714. http://dx.doi.org/10.1007/s10114-003-0283-1.

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7

Gammage, Benjamin, and Vivek Shende. "Homological mirror symmetry at large volume." Tunisian Journal of Mathematics 5, no. 1 (2023): 31–71. http://dx.doi.org/10.2140/tunis.2023.5.31.

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8

Futaki, Masahiro, and Kazushi Ueda. "Homological mirror symmetry for Brieskorn–Pham singularities." Selecta Mathematica 17, no. 2 (2011): 435–52. http://dx.doi.org/10.1007/s00029-010-0055-6.

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9

Kerr, Gabriel. "Homological mirror symmetry of elementary birational cobordisms." Selecta Mathematica 23, no. 4 (2017): 2801–47. http://dx.doi.org/10.1007/s00029-017-0325-7.

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10

Keating, Ailsa. "Homological mirror symmetry for hypersurface cusp singularities." Selecta Mathematica 24, no. 2 (2017): 1411–52. http://dx.doi.org/10.1007/s00029-017-0334-6.

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11

Tu, Junwu. "Homological Mirror Symmetry and Fourier–Mukai Transform." International Mathematics Research Notices 2015, no. 3 (2013): 579–630. http://dx.doi.org/10.1093/imrn/rnt211.

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12

Seidel, Paul. "Homological mirror symmetry for the quartic surface." Memoirs of the American Mathematical Society 236, no. 1116 (2015): 0. http://dx.doi.org/10.1090/memo/1116.

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13

Abouzaid, Mohammed, and Ivan Smith. "Homological mirror symmetry for the 4-torus." Duke Mathematical Journal 152, no. 3 (2010): 373–440. http://dx.doi.org/10.1215/00127094-2010-015.

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14

Habermann, Matthew. "Homological mirror symmetry for nodal stacky curves." Mathematical Research Letters 32, no. 1 (2025): 177–237. https://doi.org/10.4310/mrl.250708030801.

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15

Lekili, Yankı, and Alexander Polishchuk. "Homological mirror symmetry for the symmetric squares of punctured spheres." Advances in Mathematics 418 (April 2023): 108942. http://dx.doi.org/10.1016/j.aim.2023.108942.

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16

Habermann, Matthew, and Jack Smith. "Homological Berglund-Hübsch mirror symmetry for curve singularities." Journal of Symplectic Geometry 18, no. 6 (2020): 1515–74. http://dx.doi.org/10.4310/jsg.2020.v18.n6.a2.

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17

Kobayashi, Kazushi. "Remarks on the homological mirror symmetry for tori." Journal of Geometry and Physics 164 (June 2021): 104190. http://dx.doi.org/10.1016/j.geomphys.2021.104190.

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18

Abouzaid, Mohammed, та Denis Auroux. "Homological mirror symmetry for hypersurfaces in (ℂ∗)n". Geometry & Topology 28, № 6 (2024): 2825–914. http://dx.doi.org/10.2140/gt.2024.28.2825.

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19

Seidel, Paul. "Homological Mirror Symmetry for the genus two curve." Journal of Algebraic Geometry 20, no. 4 (2011): 727–69. http://dx.doi.org/10.1090/s1056-3911-10-00550-3.

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20

Ueda, Kazushi. "Homological Mirror Symmetry for Toric del Pezzo Surfaces." Communications in Mathematical Physics 264, no. 1 (2006): 71–85. http://dx.doi.org/10.1007/s00220-005-1509-0.

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21

Efimov, Alexander I. "Homological mirror symmetry for curves of higher genus." Advances in Mathematics 230, no. 2 (2012): 493–530. http://dx.doi.org/10.1016/j.aim.2012.02.022.

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22

Nohara, Yuichi, and Kazushi Ueda. "Homological mirror symmetry for the quintic 3–fold." Geometry & Topology 16, no. 4 (2012): 1967–2001. http://dx.doi.org/10.2140/gt.2012.16.1967.

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23

Bressler, Paul, and Yan Soibelman. "Homological mirror symmetry, deformation quantization and noncommutative geometry." Journal of Mathematical Physics 45, no. 10 (2004): 3972–82. http://dx.doi.org/10.1063/1.1786350.

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24

Futaki, Masahiro, and Kazushi Ueda. "Homological mirror symmetry for singularities of type D." Mathematische Zeitschrift 273, no. 3-4 (2012): 633–52. http://dx.doi.org/10.1007/s00209-012-1024-x.

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25

Hacking, Paul, and Ailsa Keating. "Homological mirror symmetry for log Calabi–Yau surfaces." Geometry & Topology 26, no. 8 (2022): 3747–833. http://dx.doi.org/10.2140/gt.2022.26.3747.

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26

Sheridan, Nick. "Formulae in noncommutative Hodge theory." Journal of Homotopy and Related Structures 15, no. 1 (2019): 249–99. http://dx.doi.org/10.1007/s40062-019-00251-2.

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AbstractWe prove that the cyclic homology of a saturated $$A_\infty $$A∞ category admits the structure of a ‘polarized variation of Hodge structures’, building heavily on the work of many authors: the main point of the paper is to present complete proofs, and also explicit formulae for all of the relevant structures. This forms part of a project of Ganatra, Perutz and the author, to prove that homological mirror symmetry implies enumerative mirror symmetry.

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27

Habermann, Matthew. "Homological mirror symmetry for invertible polynomials in two variables." Quantum Topology 13, no. 2 (2022): 207–53. http://dx.doi.org/10.4171/qt/163.

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28

Knapp, Johanna, and Harun Omer. "Matrix factorizations and homological mirror symmetry on the torus." Journal of High Energy Physics 2007, no. 03 (2007): 088. http://dx.doi.org/10.1088/1126-6708/2007/03/088.

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29

Lekili, Yankı, and Alexander Polishchuk. "Homological mirror symmetry for higher-dimensional pairs of pants." Compositio Mathematica 156, no. 7 (2020): 1310–47. http://dx.doi.org/10.1112/s0010437x20007150.

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Using Auroux’s description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^{n}$, for $k\geqslant n$, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In the case of the complement of $n+2$ generic hyperplanes in $\mathbb{C}P^{n}$ ($n$-dimensional pair of pants), we show that our partial wrapped Fukaya category is equivalent to a certain categorical resolut

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30

Fang, Bohan, Chiu-Chu Melissa Liu, David Treumann, and Eric Zaslow. "T-duality and homological mirror symmetry for toric varieties." Advances in Mathematics 229, no. 3 (2012): 1873–911. http://dx.doi.org/10.1016/j.aim.2011.10.022.

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31

Gross, Mark, and Diego Matessi. "On homological mirror symmetry of toric Calabi–Yau threefolds." Journal of Symplectic Geometry 16, no. 5 (2018): 1249–349. http://dx.doi.org/10.4310/jsg.2018.v16.n5.a3.

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32

Pascaleff, James, and Nicolò Sibilla. "Topological Fukaya category and mirror symmetry for punctured surfaces." Compositio Mathematica 155, no. 3 (2019): 599–644. http://dx.doi.org/10.1112/s0010437x19007073.

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In this paper we establish a version of homological mirror symmetry for punctured Riemann surfaces. Following a proposal of Kontsevich we model A-branes on a punctured surface$\unicode[STIX]{x1D6F4}$via the topological Fukaya category. We prove that the topological Fukaya category of$\unicode[STIX]{x1D6F4}$is equivalent to the category of matrix factorizations of a certain mirror LG model$(X,W)$. Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which are of independent interest.

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33

LAZAROIU, C. I. "D-BRANE CATEGORIES." International Journal of Modern Physics A 18, no. 29 (2003): 5299–335. http://dx.doi.org/10.1142/s0217751x03015763.

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This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic perspective, and with a focus on applications to homological mirror symmetry.

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34

Hanlon, A., and J. Hicks. "Aspects of functoriality in homological mirror symmetry for toric varieties." Advances in Mathematics 401 (June 2022): 108317. http://dx.doi.org/10.1016/j.aim.2022.108317.

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35

Chan, Kwokwai. "Homological Mirror Symmetry for Local Calabi-Yau Manifolds via SYZ." Taiwanese Journal of Mathematics 21, no. 3 (2017): 505–29. http://dx.doi.org/10.11650/tjm/7901.

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36

Ballard, Matthew, Colin Diemer, David Favero, Ludmil Katzarkov, and Gabriel Kerr. "The Mori program and Non-Fano toric Homological Mirror Symmetry." Transactions of the American Mathematical Society 367, no. 12 (2015): 8933–74. http://dx.doi.org/10.1090/s0002-9947-2015-06541-6.

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37

Sheridan, Nick. "Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space." Inventiones mathematicae 199, no. 1 (2014): 1–186. http://dx.doi.org/10.1007/s00222-014-0507-2.

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38

Katzarkov, Ludmil, and Leonardo Soriani. "Homological Mirror Symmetry, coisotropic branes and $$P=W$$ P = W." European Journal of Mathematics 4, no. 3 (2018): 1141–60. http://dx.doi.org/10.1007/s40879-018-0273-6.

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39

Borisov, Lev A., and R. Paul Horja. "Applications of homological mirror symmetry to hypergeometric systems: Duality conjectures." Advances in Mathematics 271 (February 2015): 153–87. http://dx.doi.org/10.1016/j.aim.2014.11.020.

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40

Chan, Kwokwai, Daniel Pomerleano, and Kazushi Ueda. "Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold." Communications in Mathematical Physics 341, no. 1 (2015): 135–78. http://dx.doi.org/10.1007/s00220-015-2477-7.

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41

Sheridan, Nick. "On the homological mirror symmetry conjecture for pairs of pants." Journal of Differential Geometry 89, no. 2 (2011): 271–367. http://dx.doi.org/10.4310/jdg/1324477412.

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42

Fang, Bohan. "Homological mirror symmetry is T-duality for $\mathbb{P}^n$." Communications in Number Theory and Physics 2, no. 4 (2008): 719–42. http://dx.doi.org/10.4310/cntp.2008.v2.n4.a2.

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43

Chan, Kwokwai, and Kazushi Ueda. "Dual torus fibrations and homological mirror symmetry for $A_n$-singularities." Communications in Number Theory and Physics 7, no. 2 (2013): 361–96. http://dx.doi.org/10.4310/cntp.2013.v7.n2.a5.

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44

McBreen, Michael, and Ben Webster. "Homological mirror symmetry for hypertoric varieties, I: Conic equivariant sheaves." Geometry & Topology 28, no. 3 (2024): 1005–63. http://dx.doi.org/10.2140/gt.2024.28.1005.

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45

Futaki, Masahiro, and Hiroshige Kajiura. "Homological mirror symmetry of $\mathbb{F}_1$ via Morse homotopy." Advances in Theoretical and Mathematical Physics 26, no. 8 (2022): 2611–37. http://dx.doi.org/10.4310/atmp.2022.v26.n8.a5.

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46

Futaki, Masahiro, and Hiroshige Kajiura. "Homological mirror symmetry of CPn and their products via Morse homotopy." Journal of Mathematical Physics 62, no. 3 (2021): 032307. http://dx.doi.org/10.1063/5.0029165.

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47

Chan, Kwokwai. "Homological mirror symmetry for A n -resolutions as a T -duality." Journal of the London Mathematical Society 87, no. 1 (2012): 204–22. http://dx.doi.org/10.1112/jlms/jds048.

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48

Ueda, Kazushi, and Masahito Yamazaki. "Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2013, no. 680 (2013): 1–22. http://dx.doi.org/10.1515/crelle.2012.031.

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49

Abouzaid, Mohammed. "Morse homology, tropical geometry, and homological mirror symmetry for toric varieties." Selecta Mathematica 15, no. 2 (2009): 189–270. http://dx.doi.org/10.1007/s00029-009-0492-2.

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50

Auroux, Denis. "Speculations on homological mirror symmetry for hypersurfaces in $(\mathbb{C}^{\ast})^n$." Surveys in Differential Geometry 22, no. 1 (2017): 1–47. http://dx.doi.org/10.4310/sdg.2017.v22.n1.a1.

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