Relevant bibliographies by topics / Homological mirror symmetry

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Homological mirror symmetry'

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

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Journal articles on the topic "Homological mirror symmetry"

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Homological mirror symmetry"

1

Ueda, Kazushi. "Homological mirror symmetry for toric del Pezzo surfaces." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/144153.

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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第12069号<br>理博第2963号<br>新制||理||1443(附属図書館)<br>23905<br>UT51-2006-J64<br>京都大学大学院理学研究科数学・数理解析専攻<br>(主査)助教授 河合 俊哉, 教授 齋藤 恭司, 教授 柏原 正樹<br>学位規則第4条第1項該当
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Sheridan, Nicholas (Nicholas James). "Homological mirror symmetry for a Calabi-Yau hypersurface in projective space." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73374.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 365-369).<br>This thesis is concerned with Kontsevich's Homological Mirror Symmetry conjecture. In Chapter 1, which is based on [1], we consider the n-dimensional pair of pants, which is defined to be the complement of n + 2 generic hyperplanes in CPn. The pair of pants is conjectured to be mirror to the Landau-Ginzburg model (Cn+2 , W), where W = z1...zn+2 We construct an immersed Lagrangian sphere in the pair of pants, and sho
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Books on the topic "Homological mirror symmetry"

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Castano-Bernard, Ricardo, Fabrizio Catanese, Maxim Kontsevich, Tony Pantev, Yan Soibelman, and Ilia Zharkov, eds. Homological Mirror Symmetry and Tropical Geometry. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06514-4.

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Seidel, P. Homological mirror symmetry for the quartic surface. American Mathematical Society, 2015.

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service), SpringerLink (Online, ed. Homological mirror symmetry: New developments and perspectives. Springer, 2009.

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Society, European Mathematical, ed. Fukaya categories and Picard-Lefschetz theory. European Mathematical Society, 2008.

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5

Homological Mirror Symmetry. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-68030-7.

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Bocklandt, Raf. Gentle Introduction to Homological Mirror Symmetry. University of Cambridge ESOL Examinations, 2021.

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Bocklandt, Raf. Gentle Introduction to Homological Mirror Symmetry. University of Cambridge ESOL Examinations, 2021.

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8

Catanese, Fabrizio, Maxim Kontsevich, Tony Pantev, Yan Soibelman, and Ricardo Castano-Bernard. Homological Mirror Symmetry and Tropical Geometry. Springer, 2014.

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Bocklandt, Raf. Gentle Introduction to Homological Mirror Symmetry. University of Cambridge ESOL Examinations, 2021.

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Catanese, Fabrizio, Maxim Kontsevich, Tony Pantev, Yan Soibelman, and Ricardo Castano-Bernard. Homological Mirror Symmetry and Tropical Geometry. Springer London, Limited, 2014.

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Book chapters on the topic "Homological mirror symmetry"

1

Kajiura, Hiroshige. "Homological Perturbation Theory and Homological Mirror Symmetry." In Higher Structures in Geometry and Physics. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4735-3_10.

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Harder, Andrew. "Introduction to Homological Mirror Symmetry." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91626-2_12.

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Kontsevich, Maxim. "Homological Algebra of Mirror Symmetry." In Proceedings of the International Congress of Mathematicians. Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9078-6_11.

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Givental, Alexander B. "Homological Geometry and Mirror Symmetry." In Proceedings of the International Congress of Mathematicians. Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9078-6_40.

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Katzarkov, Ludmil. "Homological Mirror Symmetry and Algebraic Cycles." In Riemannian Topology and Geometric Structures on Manifolds. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4743-8_4.

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Bejleri, Dori. "The SYZ Conjecture via Homological Mirror Symmetry." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91626-2_13.

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Katzarkov, Ludmil. "Generalized Homological Mirror Symmetry and Rationality Questions." In Cohomological and Geometric Approaches to Rationality Problems. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4934-0_7.

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"Mirror Symmetry." In A Gentle Introduction to Homological Mirror Symmetry. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108692458.011.

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"Homological mirror symmetry with higher products." In Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds. American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/023/10.

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Aganagic, Mina. "Homological knot invariants from mirror symmetry." In International Congress of Mathematicians. EMS Press, 2023. http://dx.doi.org/10.4171/icm2022/197.

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Conference papers on the topic "Homological mirror symmetry"

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KONTSEVICH, MAXIM, and YAN SOIBELMAN. "HOMOLOGICAL MIRROR SYMMETRY AND TORUS FIBRATIONS." In Proceedings of the 4th KIAS Annual International Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812799821_0007.

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Katzarkov, Ludmil. "Birational geometry and homological mirror symmetry." In Proceedings of the Australian-Japanese Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706898_0008.

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Katzarkov, L., Oscar J. Garay, Marisa Fernández, Luis Carlos de Andrés, and Luis Ugarte. "Generalized Homological Mirror Symmetry, superschemes and nonrationality." In SPECIAL METRICS AND SUPERSYMMETRY: Proceedings of the Workshop on Geometry and Physics: Special Metrics and Supersymmetry. AIP, 2009. http://dx.doi.org/10.1063/1.3089210.

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Neeman, Amnon. "An infinite version of homological mirror symmetry." In Proceedings of the Australian-Japanese Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706898_0014.

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