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We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry.
On the deformation of rings and algebras
M. Gerstenhaber · 1964
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Équations différentielles à points singuliers réguliers
P. Deligne · 1970
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Théorie de Hodge. II
P. Deligne · 1971
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Theoreme de finitude pour un morphisme propre; dimension cohommologiue des schemas algebriques affines
M. Artin · 1973
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Théorie de Hodge. III
P. Deligne · 1974
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Sur la réduction formelle des équations différentielles à singularités irrégulièrs
B. Malgrange · 1979
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Faisceaux pervers
A. Beĭlinson, J. Bernstein, and P. Deligne · 1982
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La classification des connexions irrégulières à une variable
B. Malgrange · 1983
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Period mapping associated to a primitive form
K. Saito · 1983
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Deformations of nilpotent matrices over rings and reduction of analytic families of meromorphic differential equations
D. Babbitt and V.S. Varadarajan · 1985
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Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric
G. Tian · 1987
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The Weil-Petersson geometry of the moduli space of SU ( n ≥ 3 ) {\rm SU}(n\geq 3) (Calabi-Yau) manifolds. I
A. Todorov · 1989
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Exponential sums and differential equations
N. Katz · 1990
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Sheaves on manifolds
M. Kashiwara and P. Schapira · 1990
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Enhanced triangulated categories
A. Bondal and M. Kapranov · 1991
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Topological–anti-topological fusion
S. Cecotti and C. Vafa · 1991
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On DG-modules over the de Rham complex and the vanishing cycles functor
M. Kapranov · 1991
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Équations différentielles à coefficients polynomiaux
B. Malgrange · 1991
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Unobstructed deformations. A remark on a paper of Z. Ran: “Deformations of manifolds with torsion or negative canonical bundle” [J. Algebraic Geom. 1
Y. Kawamata · 1992
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Deformations of manifolds with torsion or negative canonical bundle
Z. Ran · 1992
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Homotopy limits in triangulated categories
M. Bökstedt and A. Neeman · 1993
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Non-commutative deformations and Poisson brackets on projective spaces
A. Bondal · 1993
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Ising model and N = 2 N=2 supersymmetric theories
S. Cecotti and C. Vafa · 1993
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On classification of N = 2 N=2 supersymmetric theories
S. Cecotti and C. Vafa · 1993
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Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology
E. Getzler · 1993
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Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa · 1994
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Gromov-Witten classes, quantum cohomology, and enumerative geometry
M. Kontsevich and Yu. Manin · 1994
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Cyclic homology for schemes
C. Weibel · 1996
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The Hodge filtration on nonabelian cohomology
C. Simpson · 1997
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Mixed twistor structures
C. Simpson · 1997
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Frobenius manifolds and formality of Lie algebras of polyvector fields
S. Barannikov and M. Kontsevich · 1998
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Geometry and analytic theory of Frobenius manifolds
B. Dubrovin · 1998
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Operads and motives in deformation quantization
M. Kontsevich · 1998
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Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
J. Li and G. Tian · 1998
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Around the theory of the generalized weight system: relations with singularity theory, the generalized Weyl group and its invariant theory, etc
K. Saito · 1998
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Duality for regular systems of weights: a précis
K. Saito · 1998
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Mirror symmetry and algebraic geometry
D. Cox and S. Katz · 1999
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Frobenius manifolds, quantum cohomology, and moduli spaces
Yu. Manin · 1999
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Three constructions of Frobenius manifolds: a comparative study
Yu. Manin · 1999
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On a twisted de Rham complex
C. Sabbah · 1999
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Symplectic Gromov-Witten invariants
B. Siebert · 1999
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Mirror symmetry, 2000, hep-th/0002222
K. Hori and C. Vafa · 2000
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Deformations of algebras over operads and the Deligne conjecture
M. Kontsevich and Y. Soibelman · 2000
Cited alongside, same era.
Équations différentielles à points singuliers irréguliers et phénomène de Stokes en dimension 2
C. Sabbah · 2000
Cited alongside, same era.
Quantum periods. I. Semi-infinite variations of Hodge structures
S. Barannikov · 2001
Cited alongside, same era.
Reconstruction of a variety from the derived category and groups of autoequivalences
A. Bondal and D. Orlov · 2001
Cited alongside, same era.
Floer homology and Gromov-Witten invariants over the integers of general symplectic manifolds—summary
K. Fukaya and K. Ono · 2001
Cited alongside, same era.
Comparing K K -theories for complex varieties
E. Friedlander and M. Walker · 2001
Mirror symmetry via logarithmic degeneration data. I
M. Gross and B. Siebert · 2006
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t t ∗ tt^{*} geometry and mixed Hodge structures
C. Hertling · 2006
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Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie, 2006, preprint, arXiv.org:math/0611623
D. Kaledin · 2006
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Affine structures and non-Archimedean analytic spaces
M. Kontsevich and Y. Soibelman · 2006
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Notes on A ∞ {A}_{\infty} algebras, A ∞ {A}_{\infty} categories and non-commutative geometry. I, 2006
M. Kontsevich and Y. Soibelman · 2006
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Homological projective duality for grassmannians of lines, 2006, preprint,arXiv.org:math/0610957
A. Kuznetsov · 2006
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Cited alongside, same era.
Riemann-Roch variations
V. Golyshev · 2001
Cited alongside, same era.
Homological mirror symmetry and torus fibrations
M. Kontsevich and Y. Soibelman · 2001
Cited alongside, same era.
Non-commutative periods and mirror symmetry in higher dimensions
S. Barannikov · 2002
Cited alongside, same era.
Semi-infinite variations of Hodge structures and integrable hierarchies of KdV type
S. Barannikov · 2002
Cited alongside, same era.
Derived categories of coherent sheaves
A. Bondal and D. Orlov · 2002
Cited alongside, same era.
Déformations isomonodromiques et variétés de Frobenius
C. Sabbah · 2002
Cited alongside, same era.
Later among the works it cites.
Asymptotic behavior of tame harmonic bundles and pure twistor D D -modules
T. Mochizuki · 2006
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Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
T. Mochizuki · 2006
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Spherical functors, 2007, preprint, arXiv.org:0711.4409
R. Anno · 2007
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Mirror symmetry and T T -duality in the complement of an anticanonical divisor
D. Auroux · 2007
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Renormalisation and the Batalin-Vilkovisky formalism, 2007, arXiv.org:0706.1533
K. Costello · 2007
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Topological conformal field theories and Calabi-Yau categories
K. Costello · 2007
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Topological conformal field theories and gauge theories
K. Costello · 2007
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The Witten equation and its virtual fundamental cycle, 2007, preprint, 99 pp., arXiv.org:0712.4025
H. Fan, T. Jarvis, and Y. Ruan · 2007
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Lagrangin intersection Floer theory - anomaly and obstruction, 2007
K. Fukaya, Y.-G. Oh, H. Ohta, and K. Ono · 2007
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Classification problems and mirror duality
V. Golyshev · 2007
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Mirror symmetry via logarithmic degeneration data II, 2007, arXiv.org:0709.2290
M. Gross and B. Siebert · 2007
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Periods for irregular singular connections on surfaces
M. Hien · 2007
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Nilpotent orbits of a generalization of Hodge structures, 2007
C. Hertling and C. Sevenheck · 2007
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Real and integral structures in quantum cohomology I: toric orbifolds, 2007
H. Iritani · 2007
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A relation between the parabolic Chern characters of the de Rham bundles
J. Iyer and C. Simpson · 2007
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Cartier isomorphism and Hodge theory in the non-commutative case, 2007, preprint, arXiv.org:0708.1574
D. Kaledin · 2007
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Cyclic homology with coefficients, 2007, preprint, arXiv.org:math/0702068
D. Kaledin · 2007
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Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D D -modules. I
T. Mochizuki · 2007
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Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D D -modules. II
Takuro Mochizuki · 2007
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Directed a ∞ a_{\infty} -subcategories and natural transformations, 2007, preprint,arXiv.org:math/0701778
P. Seidel · 2007
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Fukaya categories and picard-lefschetz theory, 2007, book, 292 pp., available at http://www-math.mit.edu/ ∼ \sim seidel/revision.pdf
P. Seidel · 2007
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Algebraic interpretation of nahm transform for integrable connections, 2007
S. Szabo · 2007
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Smoothness theorem for differential BV algebras, 2007, preprint, arXiv:0707.1290
J. Terilla · 2007
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The homotopy theory of d g dg -categories and derived Morita theory
B. Toën · 2007
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Letter to the authors, May 10, 2007, 2007
B. Toën · 2007
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Letter to the authors, September 14, 2007, 2007
B. Toën · 2007
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On the Gauss-Manin connection in cyclic homology
B. Tsygan · 2007
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A counterexample to the quantizability of modules
T. Willwacher · 2007
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Duality for toric Landau-Ginzburg models, 2008, preprint, 32 pp, arXiv.org:0803.0447
P. Clarke · 2008
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Periods for flat algebraic connections, 2008, preprint,arXiv.org:0803.3463
M. Hien · 2008
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XI Solomon Lefschetz memorial lecture series: Hodge structures in non-commutative geometry. (notes by Ernesto Lupercio), 2008
M. Kontsevich · 2008
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Good formal structure for meromorphic flat connections on smooth projective surfaces, 2008, preprint, arXiv.org:0803.1346
T. Mochizuki · 2008
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Wild harmonic bundles and wild pure twistor D-modules, 2008, preprint, arXiv.org:0803.1344
T. Mochizuki · 2008
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Unobstructedness of graded Calabi-Yau categories
P. Pandit · 2008
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Hirzebruch-Riemann-Roch theorem for DG algebras
D. Shklyarov · 2008
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The Hochschild cohomology of Landau-Ginzburg models, 2008
J. Tu · 2008
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