[. Bibliographie, L. Auroux, D. Katzarkov, and . Orlov, Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves, Invent. Math, vol.166, issue.3, pp.537-582, 2006.

. Bat93, V. Victor, and . Batyrev, Quantum cohomology rings of toric manifolds

. Bat94, V. Victor, and . Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Algebraic Geom, vol.3, issue.3, pp.493-535, 1994.

A. Bayer, Semisimple quantum cohomology and blowups, Int. Math. Res. Not, issue.40, pp.2069-2083, 2004.

. A. Bcfk05, I. Bertram, B. Ciocan-fontanine, and . Kim, Two proofs of a conjecture of Hori and Vafa, Duke Mathematical Journal, vol.126, issue.1, pp.101-136, 2005.

[. Bertram, I. Ciocan-fontanine, and B. Kim, Gromov-Witten invariants for abelian and nonabelian quotients, Journal of Algebraic Geometry, vol.17, issue.2, pp.275-294, 2008.
DOI : 10.1090/S1056-3911-07-00456-0

. Bcfkvs98, V. Victor, I. Batyrev, B. Ciocan-fontanine, D. Kim et al., Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians, Nuclear Phys. B, vol.514, issue.3, pp.640-666, 1998.

. Bcfkvs00, V. Victor, I. Batyrev, B. Ciocan-fontanine, D. Kim et al., Mirror symmetry and toric degenerations of partial flag manifolds, pp.1-39, 2000.

]. A. Ber97 and . Bertram, Quantum Schubert calculus, Advances in Mathematics, vol.128, issue.2, pp.289-305, 1997.

A. Bertram, Some applications of localization to enumerative problems. Michigan Math, J, vol.48, pp.65-75, 2000.

B. [. Behrend and . Fantechi, The intrinsic normal cone, Inventiones Mathematicae, vol.128, issue.1, pp.45-88, 1997.
DOI : 10.1007/s002220050136

]. A. Bkt08a, A. Buch, H. Kresch, and . Tamvakis, A Giambelli formula for isotropic Grassmannians. Arxiv preprint math/0811, 2008.

]. A. Bkt08b, A. Buch, H. Kresch, and . Tamvakis, Quantum Giambelli formulas for isotropic Grassmannians Arxiv preprint arXiv:0812.0970, Tamvakis. Quantum Pieri rules for isotropic Grassmannians. Inventiones Mathematicae, pp.345-405, 2008.

A. Bayer and Y. I. Manin, (Semi)simple exercises in quantum cohomology, The Fano Conference, pp.143-173, 2004.

]. A. Bon89 and . Bondal, Representations of associative algebras and coherent sheaves, Izv. Akad. Nauk SSSR Ser. Mat, vol.53, issue.1, pp.25-44, 1989.

A. Borel, Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts, The Annals of Mathematics, vol.57, issue.1, pp.115-207, 1953.
DOI : 10.2307/1969728

]. N. Bou68 and . Bourbaki, Eléments de mathématiques, fasc. 34: groupes et algèbres de Lie, 1968.

]. A. Buc03 and . Buch, Quantum cohomology of Grassmannians, Compositio Mathematica, vol.137, issue.2, pp.227-235, 2003.

[. Ciocan-fontanine, On quantum cohomology rings of partial flag varieties, Duke Mathematical Journal, vol.98, issue.3, pp.485-524, 1999.
DOI : 10.1215/S0012-7094-99-09815-0

G. Ciolli, ON THE QUANTUM COHOMOLOGY OF SOME FANO THREEFOLDS AND A CONJECTURE OF DUBROVIN, International Journal of Mathematics, vol.16, issue.08, pp.823-839, 2005.
DOI : 10.1142/S0129167X05003144

A. David, S. Cox, and . Katz, Mirror symmetry and algebraic geometry, volume 68 of Mathematical Surveys and Monographs, 1999.

P. Chaput, L. Manivel, and N. Perrin, Quantum Cohomology of Minuscule Homogeneous Spaces II Hidden Symmetries, International Mathematics Research Notices, vol.29, issue.22, 2007.
DOI : 10.1093/imrn/rnm107

URL : https://hal.archives-ouvertes.fr/hal-00101905

P. E. Chaput, L. Manivel, and N. Perrin, Quantum cohomology of minuscule homogeneous spaces. Transform. Groups, pp.47-89, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00086927

P. Chaput, L. Manivel, and N. Perrin, Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces, Mathematical Research Letters, vol.16, issue.1, pp.7-211246, 2009.
DOI : 10.4310/MRL.2009.v16.n1.a2

URL : https://hal.archives-ouvertes.fr/hal-01256776

I. Coskun, A Littlewood-Richardson rule for partial flag varieties

[. Coskun, A Littlewood???Richardson rule for two-step flag varieties, Inventiones mathematicae, vol.164, issue.15, pp.325-395, 2009.
DOI : 10.1007/s00222-008-0165-3

N. [. Chaput and . Perrin, On the quantum cohomology of adjoint varieties. Arxiv preprint arXiv, pp.904-4824, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01256756

[. Concini and C. Procesi, Complete symmetric varieties. II. Intersection theory. In Algebraic groups and related topics, Adv. Stud. Pure Math, vol.6, pp.481-513, 1983.

[. Duan and B. Li, Topology of Blow-ups and Enumerative Geometry. Arxiv preprint arXiv, pp.906-4152, 2009.

[. Dubrovin, Painlev?? Transcendents in Two-Dimensional Topological Field Theory, The Painlevé property, pp.287-412, 1999.
DOI : 10.1007/978-1-4612-1532-5_6

R. [. Fulton and . Pandharipande, Notes on stable maps and quantum cohomology, Algebraic geometry?Santa Cruz 1995, Proc. Sympos. Pure Math, pp.45-96, 1997.

W. Fulton, Intersection Theory, 1984.

W. Fulton and . Young, With applications to representation theory and geo- metry, 1997.

C. [. Fulton and . Woodward, On the quantum product of Schubert classes, Journal of Algebraic Geometry, vol.13, issue.4, pp.641-661, 2004.
DOI : 10.1090/S1056-3911-04-00365-0

A. B. Givental, Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices, issue.13, pp.613-663, 1996.

A. Givental, A mirror theorem for toric complete intersections In Topological field theory, primitive forms and related topics, Progr. Math. Birkhäuser Boston, vol.160, pp.141-175, 1996.

A. B. Givental, Gromov-Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J, vol.1, issue.645, pp.551-568, 2001.

A. Givental and B. Kim, Quantum cohomology of flag manifolds and Toda lattices, Communications in Mathematical Physics, vol.17, issue.2, pp.609-641, 1995.
DOI : 10.1007/BF02101846

]. A. Gor90 and . Gorodentsev, Exceptional objects and mutations in derived categories, Helices and vector bundles, pp.57-73, 1990.

T. Graber, Enumerative geometry of hyperelliptic plane curves, J. Algebraic Geom, vol.10, issue.4, pp.725-755, 2001.

D. Guzzetti, Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces, Communications in Mathematical Physics, vol.207, issue.2, pp.341-383, 1999.
DOI : 10.1007/s002200050729

?. [. Gel and A. V. Fand, Zelevinski? ?. Models of representations of classical groups and their hidden symmetries, Funktsional. Anal. i Prilozhen, vol.18, issue.3, pp.14-31, 1984.

A. Hatcher, Algebraic topology, 2002.

Y. [. Hertling, C. Manin, and . Teleman, An update on semisimple quantum cohomology and F-manifolds, Proceedings of the Steklov Institute of Mathematics, vol.264, issue.1, pp.69-76, 2009.
DOI : 10.1134/S0081543809010088

M. [. Hille and . Perling, A counterexample to King's conjecture, Compositio Mathematica, vol.142, issue.06, pp.1507-1521, 2006.
DOI : 10.1112/S0010437X06002260

]. D. Huy06 and . Huybrechts, Fourier-Mukai transforms in algebraic geometry. Oxford Mathematical Monographs, 2006.

H. Iritani, Convergence of quantum cohomology by quantum Lefschetz, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2007, issue.610, pp.29-69, 2007.
DOI : 10.1515/CRELLE.2007.067

H. Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Advances in Mathematics, vol.222, issue.3, pp.1016-1079, 2009.
DOI : 10.1016/j.aim.2009.05.016

]. M. Kap88 and . Kapranov, On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math, vol.92, issue.3, pp.479-508, 1988.

Y. Kawamata, Derived categories of toric varieties. Michigan Math, J, vol.54, issue.3, pp.517-535, 2006.

[. Kim, Quantum hyperplane section theorem for homogeneous spaces, Acta Mathematica, vol.183, issue.1, pp.71-99, 1999.
DOI : 10.1007/BF02392947

URL : http://arxiv.org/abs/alg-geom/9712008

]. A. Kin97 and . King, Tilting bundles on some rational surfaces. Unpublished manuscript, 1997.

]. S. Kle74 and . Kleiman, The transversality of a general translate, Compositio Math, vol.28, pp.287-297, 1974.

Y. [. Kontsevich and . Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Communications in Mathematical Physics, vol.1, issue.3, pp.525-562, 1994.
DOI : 10.1007/BF02101490

D. [. Kuleshov and . Orlov, Exceptional sheaves on Del Pezzo surfaces [Kon95a] Maxim Kontsevich. Enumeration of rational curves via torus actions, The moduli space of curves, pp.53-87, 1994.
DOI : 10.1070/im1995v044n03abeh001609

[. Kontsevich, Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians, pp.120-139, 1994.

A. Kresch and H. Tamvakis, Quantum cohomology of the Lagrangian Grassmannian, Journal of Algebraic Geometry, vol.12, issue.4, pp.777-810, 2003.
DOI : 10.1090/S1056-3911-03-00347-3

]. A. Kuz06 and . Kuznetsov, Hyperplane sections and derived categories, Izv. Ross. Akad. Nauk Ser. Mat, vol.70, issue.3, pp.23-128, 2006.

A. Kuznetsov, Exceptional collections for Grassmannians of isotropic lines, Proc. LondLL] Naichung Conan Leung and Changzheng Li. Quantum Pieri rules for tautological subbundles, pp.155-182, 2008.
DOI : 10.1112/plms/pdm056

[. , C. Leung, C. Li, and Q. , Functorial relationships between QH, J. Differential Geom, vol.86, issue.2, pp.303-354, 2010.

B. H. Lian, K. Liu, and S. Yau, Mirror principle I, Asian Journal of Mathematics, vol.1, issue.4, pp.729-763, 1997.
DOI : 10.4310/AJM.1997.v1.n4.a5

[. Lam and M. Shimozono, Quantum cohomology of G/P and homology of affine Grassmannian, Acta Mathematica, vol.204, issue.1, pp.49-90, 2010.
DOI : 10.1007/s11511-010-0045-8

J. Li and G. Tian, Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties, Journal of the American Mathematical Society, vol.11, issue.01, pp.119-174, 1998.
DOI : 10.1090/S0894-0347-98-00250-1

I. G. Macdonald, Symmetric functions and Hall polynomials, 1979.

[. Manivel, Fonctions symétriques, polynômes de Schubert et lieux de dégénérescence, of Cours Spécialisés [Specialized Courses]. Société Mathématique de France, 1998.

]. L. Man11 and . Manivel, On the derived category of the Cayley plane, J. Algebra, vol.330, pp.177-187, 2011.

]. M. Mic10 and . Michalek, Family of counterexamples to king's conjecture, Comptes Rendus Mathematique, 2010.

]. I. Mih07 and . Mihai, Odd symplectic flag manifolds. Transformation groups, pp.573-599, 2007.

]. S. Mit08 and . Mitchell, Parabolic orbits in flag varieties. preprint, 1, 2008.

]. D. Orl92 and . Orlov, Projective bundles, monoidal transformations, and derived categories of coherent sheaves, Izv. Ross. Akad. Nauk Ser. Mat, vol.56, issue.4, pp.852-862, 1992.

[. Perrin, Rational curves on homogeneous varieties, Annales de l???institut Fourier, vol.52, issue.1
DOI : 10.5802/aif.1878

D. Pontoni, Quantum cohomology of $\text{\normalfont H\lowercase{ilb}}^2(\mathbb{P}^1 \times\mathbb{P}^1)$ and enumerative applications, Transactions of the American Mathematical Society, vol.359, issue.11, pp.5419-5448, 2007.
DOI : 10.1090/S0002-9947-07-04169-4

P. Pragacz and J. Ratajski, A Pieri-type theorem for Lagrangian and odd orthogonal Grassmannians, J. Reine Angew. Math, vol.476, pp.143-189, 1996.

P. Pragacz, J. Robert, and A. Proctor, A Pieri-type formula for even orthogonal Grassmannians, Lie algebras and related topics of CMS Conf. Proc, pp.49-96, 1984.
DOI : 10.4064/fm178-1-2

]. V. Prz07 and . Przyjalkowski, Gromov-Witten invariants of Fano threefolds of genera 6 and 8, Sbornik: Mathematics, vol.198, p.433, 2007.

A. Polishchuk and A. Samokhin, Full exceptional collections on the lagrangian grassmannians LG(4, 8) and LG(5, 10) Arxiv preprint arXiv, pp.910-2356, 2009.

A. Polishchuk and E. Zaslow, Categorical mirror symmetry: The elliptic curve, Winter School on Mirror Symmetry, pp.275-295, 1999.
DOI : 10.4310/ATMP.1998.v2.n2.a9

[. Ruan and G. Tian, A mathematical theory of quantum cohomology, Mathematical Research Letters, vol.1, issue.2, pp.269-278, 1994.
DOI : 10.4310/MRL.1994.v1.n2.a15

A. Samokhin, Some remarks on the derived categories of coherent sheaves on homogeneous spaces, Journal of the London Mathematical Society, vol.76, issue.1, pp.122-134, 2007.
DOI : 10.1112/jlms/jdm038

[. Siebert and G. Tian, On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator, Asian Journal of Mathematics, vol.1, issue.4, pp.679-695, 1997.
DOI : 10.4310/AJM.1997.v1.n4.a2

]. H. Tam07 and . Tamvakis, Quantum cohomology of homogeneous varieties: a survey, 2007.

]. C. Tel07 and . Teleman, The structure of 2d semi-simple field theories. Arxiv preprint, 2007.

]. K. Ued05a and . Ueda, Stokes matrix for the quantum cohomology of cubic surfaces. Arxiv preprint math/0505350, 2005.

K. Ueda, Stokes matrices for the quantum cohomologies of Grassmannians, Int. Math. Res. Not, issue.34, pp.2075-2086, 2005.

A. Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Inventiones Mathematicae, vol.58, issue.3, pp.613-670, 1989.
DOI : 10.1007/BF01388892

E. Witten, Two-dimensional gravity and intersection theory on moduli space In Surveys in differential geometry, Lehigh Univ, pp.243-310, 1990.

E. Witten, The Verlinde algebra and the cohomology of the Grassmannian In Geometry, topology, & physics, Proc. Lecture Notes Geom. Topology, IV, pp.357-422, 1995.