Relevant bibliographies by topics / Mirror symmetry

Academic literature on the topic 'Mirror symmetry'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 March 2023

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Contents

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

Journal articles on the topic "Mirror symmetry":

1

Ma, Zhi Yong. "Research on Concept System of Rotation-Mirror Symmetry in Mechanical Systems." Applied Mechanics and Materials 201-202 (October 2012): 7–10. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.7.

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Mechanical rotation-mirror symmetry is grouped by rotation symmetry and mirror symmetry, and belongs to mechanical static structure symmetry. Collecting and Analyzing a lot of rotation-mirror symmetric instances, and referring to the researches on concept systems of rotation symmetry and mirror symmetry, the concept system of rotation-mirror symmetry was established. The concept system is classified by discrete mirror and continuous mirror rotation-mirror symmetry, unidirectional rotation and bidirectional rotation rotation-mirror symmetry, directed rotation and deflecting rotation rotation-mirror symmetry, entire rotation and partial rotation rotation-mirror symmetry. The concept system can completely contain all kinds of existence of rotation-mirror symmetry in mechanical systems.
2

Takahashi, Nobuyoshi. "Log Mirror Symmetry and Local Mirror Symmetry." Communications in Mathematical Physics 220, no. 2 (July 2001): 293–99. http://dx.doi.org/10.1007/pl00005567.

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Blumenhagen, Ralph, Rolf Schimmrigk, and Andreas Wiβkirchen. "(0,2) Mirror symmetry." Nuclear Physics B 486, no. 3 (February 1997): 598–628. http://dx.doi.org/10.1016/s0550-3213(96)00698-0.

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Gross, Mark. "Topological mirror symmetry." Inventiones mathematicae 144, no. 1 (April 2001): 75–137. http://dx.doi.org/10.1007/s002220000119.

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Wan, Daqing. "Arithmetic Mirror Symmetry." Pure and Applied Mathematics Quarterly 1, no. 2 (2005): 369–78. http://dx.doi.org/10.4310/pamq.2005.v1.n2.a7.

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Zhang, Jun, and Gabriel Khan. "Statistical mirror symmetry." Differential Geometry and its Applications 73 (December 2020): 101678. http://dx.doi.org/10.1016/j.difgeo.2020.101678.

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7

Ma, Zhi Yong. "Research on Concept System of Mechanical Glide Symmetry." Applied Mechanics and Materials 151 (January 2012): 433–37. http://dx.doi.org/10.4028/www.scientific.net/amm.151.433.

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As one kind of mechanical static structure symmetry, glide symmetry is grouped by mirror symmetry and translation symmetry. Glide symmetry is widely exists in mechanical systems, and plays an important role in realizing the technical, economic and social performances of mechanical products. On the basis of research on the concept systems of mirror symmetry, translation symmetry and glide symmetric instances, and taking the characters of the different combined types of symmetry benchmarks as the standard, the concept system of mechanical glide symmetry was established, which can be the foundation of further researches on the application laws of glide symmetry in mechanical systems.
8

MELKEMI, MAHMOUD, FREDERIC CORDIER, and NICKOLAS S. SAPIDIS. "A PROVABLE ALGORITHM TO DETECT WEAK SYMMETRY IN A POLYGON." International Journal of Image and Graphics 13, no. 01 (January 2013): 1350002. http://dx.doi.org/10.1142/s0219467813500022.

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This paper deals with the problem of detecting "weak symmetry" in a polygon, which is a special bijective and continuous mapping between the vertices of the given polygon. An application of this work is the automatic reconstruction of 3D polygons symmetric with respect to a plane from free-hand sketches of weakly-symmetric 2D polygons. We formalize the weak-symmetry notion and highlight its many properties which lead to an algorithm detecting it. The closest research work to the proposed approach is the detection of skewed symmetry. Skewed symmetry detection deals only with reconstruction of planar mirror-symmetric 3D polygons while our method is able to identify symmetry in projections of planar as well as nonplanar mirror-symmetric 3D polygons.
9

Giveon, Amit, and Edward Witten. "Mirror symmetry as a gauge symmetry." Physics Letters B 332, no. 1-2 (July 1994): 44–50. http://dx.doi.org/10.1016/0370-2693(94)90856-7.

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DUNDEE, B., J. PERKINS, and G. CLEAVER. "OBSERVABLE/HIDDEN SECTOR BROKEN SYMMETRY FOR SYMMETRIC BOUNDARY CONDITIONS." International Journal of Modern Physics A 21, no. 16 (June 30, 2006): 3367–85. http://dx.doi.org/10.1142/s0217751x06031090.

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A four-dimensional heterotic string model of free fermionic construction is presented wherein mirror symmetry breaking between observable and hidden sector gauge groups occurs in spite of mirror symmetry between observable and hidden sector worldsheet fermion boundary conditions. The differentiation is invoked by an asymmetry in GSO projections necessarily resulting from the symmetry of the free fermionic boundary conditions. In the specific examples shown, an expected nonchiral Pati–Salam mirror universe model is transformed into a chiral model with enhanced hidden sector gauge symmetry and reduced observable sector gauge symmetry: [ SU (4)C ⊗ SU (2)L ⊗ SU (2)R]O ⊗ [ SU (4)C ⊗ SU (2)L ⊗ SU (2)R]H, is necessarily transformed into a chiral [ SU (4)C ⊗ SU (2)L]O ⊗ [ SO (10) ⊗ SU (2)R]H model because of an unavoidable asymmetry in GSO projections.
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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Mirror symmetry":

1

Branco, Lucas Castello. "Higgs bundles, Lagrangians and mirror symmetry." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:612325bd-6a7f-4d74-a85c-426b73ff7a14.

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Let Σ be a compact Riemann surface of genus g ≥ 2. This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space. After recalling basic facts in the first chapter about G-Higgs bundles for a reductive group G, we begin the first part of the work, which deals with Higgs bundles for the real forms G0 = SU* (2m), SO* (4m), and Sp(m, m) of G = SL(2m, C), SO(4m, C) and Sp(4m, C), respectively. The second part of the thesis deals with the Gaiotto Lagrangian. Motivated by mirror symmetry, we give a detailed description of the fibres of the G-Hitchin fibration containing generic G0-Higgs bundles, for the real groups G0 = SU* (2m), SO* (4m) and Sp(m, m). The spectral curves associated to these fibres are examples of ribbons, i.e., non-reduced projective C-schemes of dimension one, whose reduced scheme are non-singular. Our description of these fibres is done in two different ways, each giving different and interesting insights about the fibre in question. One of the formulations is given in term of objects on the reduced curve, while the other in terms of the non-reduced spectral curve. A link is also provided between the two approaches. We use this description to give a proposal for the support of the dual BBB-brane inside the moduli space M(LG) of Higgs bundles for the Langlands dual group LG of G. In the second part of the thesis we discuss the Gaiotto Lagrangian, which is a Lagrangian subvariety of the moduli spaces of G-Higgs bundles, where G is a reductive group over C. This Lagrangian is obtained from a symplectic representation of G and we discuss some of its general properties. In Chapter 7 we focus our attention to the Gaiotto Lagrangian for the standard representation of the symplectic group. This is an irreducible component of the nilpotent cone for the symplectic Hitchin fibration. We describe this component by using the usual Morse function on the Higgs bundle moduli space, which is the norm squared of the Higgs field restricted to the Lagrangian in question. Lastly, we discuss natural questions and applications of the ideas developed in this thesis. In particular, we say a few words about the hyperholomorphic bundle, how to generalize the Gaiotto Lagrangian to vector bundles which admit many sections and give an analogue of the Gaiotto Lagrangian for the orthogonal group.
2

Mertens, Adrian. "Mirror Symmetry in the presence of Branes." Diss., lmu, 2011. http://nbn-resolving.de/urn:nbn:de:bvb:19-135464.

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Gu, Wei. "Gauged Linear Sigma Model and Mirror Symmetry." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90892.

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This thesis is devoted to the study of gauged linear sigma models (GLSMs) and mirror symmetry. The first chapter of this thesis aims to introduce some basics of GLSMs and mirror symmetry. The second chapter contains the author's contributions to new exact results for GLSMs obtained by applying supersymmetric localization. The first part of that chapter concerns supermanifolds. We use supersymmetric localization to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to corresponding Atwisted GLSM correlation functions for hypersurfaces. The second part of that chapter defines associated Cartan theories for non-abelian GLSMs by studying partition functions as well as elliptic genera. The third part of that chapter focuses on N=(0,2) GLSMs. For those deformed from N=(2,2) GLSMs, we consider A/2-twisted theories and formulate the genuszero correlation functions in terms of Jeffrey-Kirwan-Grothendieck residues on Coulomb branches, which generalize the Jeffrey-Kirwan residue prescription relevant for the N=(2,2) locus. We reproduce known results for abelian GLSMs, and can systematically calculate more examples with new formulas that render the quantum sheaf cohomology relations and other properties manifest. We also include unpublished results for counting deformation parameters. The third chapter is about mirror symmetry. In the first part of the third chapter, we propose an extension of the Hori-Vafa mirrror construction [25] from abelian (2,2) GLSMs they considered to non-abelian (2,2) GLSMs with connected gauge groups, a potential solution to an old problem. We formally show that topological correlation functions of B-twisted mirror LGs match those of A-twisted gauge theories. In this thesis, we study two examples, Grassmannians and two-step flag manifolds, verifying in each case that the mirror correctly reproduces details ranging from the number of vacua and correlations functions to quantum cohomology relations. In the last part of the third chapter, we propose an extension of the Hori-Vafa construction [25] of (2,2) GLSM mirrors to (0,2) theories obtained from (2,2) theories by special tangent bundle deformations. Our ansatz can systematically produce the (0,2) mirrors of toric varieties and the results are consistent with existing examples which were produced by laborious guesswork. The last chapter briefly discusses some directions that the author would like to pursue in the future.
Doctor of Philosophy
In this thesis, I summarize my work on gauged linear sigma models (GLSMs) and mirror symmetry. We begin by using supersymmetric localization to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to corresponding A-twisted GLSM correlation functions for hypersurfaces. We also define associated Cartan theories for non-abelian GLSMs. We then consider N =(0,2) GLSMs. For those deformed from N =(2,2) GLSMs, we consider A/2-twisted theories and formulate the genus-zero correlation functions on Coulomb branches. We reproduce known results for abelian GLSMs, and can systematically compute more examples with new formulas that render the quantum sheaf cohomology relations and other properties are manifest. We also include unpublished results for counting deformation parameters. We then turn to mirror symmetry, a duality between seemingly-different two-dimensional quantum field theories. We propose an extension of the Hori-Vafa mirror construction [25] from abelian (2,2) GLSMs to non-abelian (2,2) GLSMs with connected gauge groups, a potential solution to an old problem. In this thesis, we study two examples, Grassmannians and two-step flag manifolds, verifying in each case that the mirror correctly reproduces details ranging from the number of vacua and correlations functions to quantum cohomology relations. We then propose an extension of the HoriVafa construction [25] of (2,2) GLSM mirrors to (0,2) theories obtained from (2,2) theories by special tangent bundle deformations. Our ansatz can systematically produce the (0,2) mirrors of toric varieties and the results are consistent with existing examples. We conclude with a discussion of directions that we would like to pursue in the future.
4

Perevalov, Eugene V. "Type II/heterotic duality and mirror symmetry /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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5

Rossi, Paolo. "Symplectic Topology, Mirror Symmetry and Integrable Systems." Doctoral thesis, SISSA, 2008. http://hdl.handle.net/11577/3288900.

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Using Sympelctic Field Theory as a computational tool, we compute Gromov-Witten theory of target curves using gluing formulas and quantum integrable systems. In the smooth case this leads to a relation of the results of Okounkov and Pandharipande with the quantum dispersionless KdV hierarchy, while in the orbifold case we prove triple mirror symmetry between GW theory of target P^1 orbifolds of positive Euler characteristic, singularity theory of a class of polynomials in three variables and extended affine Weyl groups of type ADE.
6

Krefl, Daniel. "Real Mirror Symmetry and The Real Topological String." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-102832.

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7

Williams, Matthew Michael. "Mirror Symmetry for Non-Abelian Landau-Ginzburg Models." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/8560.

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We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.
8

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)
0048
新制・課程博士
博士(理学)
甲第12069号
理博第2963号
新制||理||1443(附属図書館)
23905
UT51-2006-J64
京都大学大学院理学研究科数学・数理解析専攻
(主査)助教授 河合 俊哉, 教授 齋藤 恭司, 教授 柏原 正樹
学位規則第4条第1項該当
9

Kadir, Shabnam Nargis. "The arithmetic of Calabi-Yau manifolds and mirror symmetry." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403756.

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Petracci, Andrea. "On Mirror Symmetry for Fano varieties and for singularities." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/55877.

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In this thesis we discuss some aspects of Mirror Symmetry for Fano varieties and toric singularities. We formulate a conjecture that relates the quantum cohomology of orbifold del Pezzo surfaces to a power series that comes from Fano polygons. We verify this conjecture in some cases, in joint work with A. Oneto. We generalise the Altmann–Mavlyutov construction of deformations of toric singularities: from Minkowski sums of polyhedra we construct deformations of affine toric pairs. Moreover, we propose an approach to the study of deformations of Gorenstein toric singularities of dimension 3 in the context of the Gross–Siebert program. We construct deformations of polarised projective toric varieties by deforming their affine cones. This method is explicit in terms of Cox coordinates and it allows us to give explicit equations for a construction, due to Ilten, which produces a deformation between two toric Fano varieties when their corresponding polytopes are mutation equivalent. We also provide examples of Gorenstein toric Fano 3-folds which are locally smoothable, but not globally smoothable.
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Books on the topic "Mirror symmetry":

1

Voisin, C. Mirror symmetry. Providence, RI: American Mathematical Society, 1999.

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Kentaro, Hori, ed. Mirror symmetry. Providence, RI: American Mathematical Society, 2003.

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Jinzenji, Masao. Classical Mirror Symmetry. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0056-1.

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4

1963-, Greene B., and Yau Shing-Tung 1949-, eds. Mirror symmetry II. Providence, RI: American Mathematical Society, 1997.

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1949-, Yau Shing-Tung, ed. Mirror symmetry I. Providence, RI: American Mathematical Society, 1998.

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Castaño-Bernard, Ricardo, Yan Soibelman, and Ilia Zharkov, eds. Mirror Symmetry and Tropical Geometry. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/conm/527.

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7

Cox, David A. Mirror symmetry and algebraic geometry. Providence, R.I: American Mathematical Society, 1999.

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1964-, Aspinwall Paul, ed. Dirichlet branes and mirror symmetry. Providence, R.I: American Mathematical Society, 2009.

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9

Bunch, Bryan H. Reality's mirror: Exploring the mathematics of symmetry. New York: Wiley, 1989.

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10

Conference on Complex Geometry and Mirror Symmetry (1995 Montréal, Québec). Mirror symmetry III: Proceedings of the Conference on Complex Geometry and Mirror Symmetry, Montréal, 1995. Edited by Phong Duong H. 1953-, Vinet Luc, and Yau Shing-Tung 1949-. Providence, R.I: American Mathematical Society, 1998.

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Book chapters on the topic "Mirror symmetry":

1

Berman, David, Hugo Garcia-Compean, Paulius Miškinis, Miao Li, Daniele Oriti, Steven Duplij, Steven Duplij, et al. "Mirror Symmetry." In Concise Encyclopedia of Supersymmetry, 241. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_320.

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Talpo, Mattia. "Batyrev Mirror Symmetry." In Springer Proceedings in Mathematics & Statistics, 103–13. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91626-2_9.

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Cox, David, and Sheldon Katz. "Mirror symmetry constructions." In Mathematical Surveys and Monographs, 53–72. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/surv/068/04.

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Clader, Emily, and Yongbin Ruan. "Mirror Symmetry Constructions." In B-Model Gromov-Witten Theory, 1–77. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94220-9_1.

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Jinzenji, Masao. "Brief History of Classical Mirror Symmetry." In Classical Mirror Symmetry, 1–26. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0056-1_1.

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Jinzenji, Masao. "Basics of Geometry of Complex Manifolds." In Classical Mirror Symmetry, 27–53. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0056-1_2.

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Jinzenji, Masao. "Topological Sigma Models." In Classical Mirror Symmetry, 55–81. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0056-1_3.

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Jinzenji, Masao. "Details of B-Model Computation." In Classical Mirror Symmetry, 83–108. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0056-1_4.

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Jinzenji, Masao. "Reconstruction of Mirror Symmetry Hypothesis from a Geometrical Point of View." In Classical Mirror Symmetry, 109–40. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0056-1_5.

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"Mirror Symmetry." In Visual Symmetry, 5–30. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835321_0001.

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Conference papers on the topic "Mirror symmetry":

1

Ge, Li. "Complex Mirror Symmetry in Optics." In Frontiers in Optics. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/fio.2018.jw3a.51.

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HACKING, PAUL, and SEAN KEEL. "MIRROR SYMMETRY AND CLUSTER ALGEBRAS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0073.

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Thomas, Richard P. "An Exercise in Mirror Symmetry." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0067.

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DE LA OSSA, XENIA. "CALABI-YAU MANIFOLDS AND MIRROR SYMMETRY." In Proceedings of the Tenth General Meeting. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704276_0009.

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Lenzi, Silvia, and Rita Lau. "Mirror (a)symmetry far from stability." In 10th Latin American Symposium on Nuclear Physics and Applications. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.194.0035.

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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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Nahm, Werner. "Mirror symmetry and self-duality equations." In Non-perturbative Quantum Effects 2000. Trieste, Italy: Sissa Medialab, 2000. http://dx.doi.org/10.22323/1.006.0023.

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Mestetskiy, L., and A. Zhuravskaya. "Mirror Symmetry Detection in Digital Images." In 15th International Conference on Computer Vision Theory and Applications. SCITEPRESS - Science and Technology Publications, 2020. http://dx.doi.org/10.5220/0008976003310337.

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Beradze, Revaz, and Merab Gogberashvili. "LIGO signals from mirror world." In RDP online PhD school and workshop "Aspects of Symmetry". Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.412.0029.

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Reports on the topic "Mirror symmetry":

1

Kachru, Shamit. Mirror Symmetry for Open Strings. Office of Scientific and Technical Information (OSTI), June 2000. http://dx.doi.org/10.2172/763790.

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Sin, Sang-Jin. Chiral Rings, Mirror Symmetry and the Fate of Localized Tachyons. Office of Scientific and Technical Information (OSTI), March 2003. http://dx.doi.org/10.2172/812956.

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Chuang, W. A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy. Office of Scientific and Technical Information (OSTI), June 2004. http://dx.doi.org/10.2172/827006.

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Hua, D., and T. Fowler. SYMTRAN - A Time-dependent Symmetric Tandem Mirror Transport Code. Office of Scientific and Technical Information (OSTI), June 2004. http://dx.doi.org/10.2172/15014290.

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