Андрей Окуньков

профессор / Сколковский институт науки и технологий
профессор / Колумбийский университет

Профессиональные интересы:
Теория представлений и её приложения к алгебраической геометрии, математическая физика, теория вероятностей и теория специальных функций.

Образование, учёные степени
1993 / Московский государственный университет, механико-математический факультет / специальность “Математика. Прикладная математика”
1995 / Кандидат физико-математических наук / Московский государственный университет / математика,

В 2004 году присуждена Премия Европейского математического общества.
В 2006 г. удостоен Филдсовской медали “за достижения, соединяющие теорию вероятностей, теорию представлений и алгебраическую геометрию”.

В 2014 года стал одним из научных руководителей международной лаборатории теории представлений и математической физики факультета математики Высшей школы экономики

Основные публикации

  1. A. Oblomkov, A. Okounkov, R. Pandharipande, “GW/PT descendent correspondence via vertex operators”, [ PDF: English, arXiv: 1806.00714 ]
  2. A. Okounkov, “Takagi lectures on Donaldson-Thomas theory”, [ PDF: English, arXiv: 1802.00779 ]
  3. A. Okounkov, “On the crossroads of enumerative geometry and geometric representation theory”, [ PDF: English, arXiv: 1801.09818 ]
  4. M. Aganagic, A. Okounkov, “Quasimap counts and Bethe eigenfunctions”, [ PDF: English, arXiv: 1704.08746 ]
  5. M. Aganagic, E. Frenkel, A. Okounkov, “Quantum q-Langlands Correspondence”, [ PDF: English, arXiv: 1701.03146 ]
  6. A. Okounkov, “Enumerative geometry and geometric representation theory”, [ PDF: English, arXiv: 1701.00713 ]
  7. M. Aganagic, A. Okounkov, “Elliptic stable envelope”, [ PDF: English, arXiv: 1604.00423 ]
  8. A. Okounkov, A. Smirnov, “Quantum difference equation for Nakajima varieties”, [ PDF: English, arXiv: 1602.09007 ]
  9. A. Okounkov, “Limit shapes, real and imagined”, Bulletin of the American Mathematical Society( New Series). 2016. Vol. 53. No. 2. P. 187-216.
  10. N. Nekrasov, A. Okounkov, “Membranes and sheaves”, Algebraic Geometry. 2016. Vol. 3. No. 3-76.
  11. A. Okounkov, E. Rains, “Noncommutative geometry and Painleve equations”, Algebra and Number Theory, 2015. [ PDF: English, arXiv: 1404.5938 ]
  12. A. Okounkov, “Lectures on K-theoretic computations in enumerative geometry”, [ PDF: English, arXiv: 1512.07363 ]
  13. А. Окуньков, “Схемы Гильберта и кратные q-дзета-значения”, Функц. анализ и его прил., 48:2 (2014), 79–87. “Hilbert schemes and multiple q-zeta values” [ PDF: English, arXiv: 1404.3873 ]
  14. E. Carlsson, N. Nekrasov, A. Okounkov, “Five dimensional gauge theories and vertex operators”, Mosc. Math. J., 14:1 (2014), 39–61.
  15. N. Nekrasov, A. Okounkov, “Membranes and Sheaves”, [ PDF: English, arXiv: 1404.2323 ]
  16. E. Carlsson, N. Nekrasov, A. Okounkov, “Five dimensional gauge theories and vertex operators”, [ PDF: English, arXiv: 1308.2465 ]
  17. D. Maulik, A. Okounkov, “Quantum Groups and Quantum Cohomology”, [ PDF: English, arXiv: 1211.1287 ]
  18. A. Braverman, D. Maulik, A. Okounkov, “Quantum cohomology of the Springer resolution”, [ PDF: English, arXiv: 1001.0056 ]
  19. A. Okounkov, “Noncommutative geometry of random surfaces”, [ PDF: English, arXiv: 0907.2322 ]
  20. A. Okounkov, R. Pandharipande, “The quantum differential equation of the Hilbert scheme of points in the plane”, Transformation Groups, 2010. Vol. 15. No. 4, 965-982. [ PDF: English, arXiv: 0906.3587 ]
  21. J. Bryan, R. Pandharipande, C. Faber, A. Okounkov, “The local Gromov-Witten theory of curves”, J American Math Soc, 2008. No. 21, 101-136.
  22. D. Maulik, A. Oblomkov, A. Okounkov, R. Pandharipande, “Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds”, [ PDF: English, arXiv: 0809.3976 ]
  23. G. Mikhalkin, A. Okounkov, “Geometry of planar log-fronts”, Mosc. Math. J., 7:3 (2007), 507–531.
  24. E. Carlsson, A. Okounkov, “Exts and Vertex Operators”, [ PDF: English, arXiv: 0801.2565 ]
  25. G. Mikhalkin, A. Okounkov, “Geometry of planar log-fronts”, [ PDF: English, arXiv: math/0608018 ]
  26. A. Okounkov, G. Olshanski, “Limits of BC-type orthogonal polynomials as the number of variables goes to infinity”, Jack, Hall-Littlewood and Macdonald Polynomials (E.B.Kuznetsov and S.Sahi,eds). Amer. Math. Soc., Contemporary Math. vol. 417, 2006 [ PDF: English, arXiv: math/0606085 ]
  27. A. Okounkov, “Random partitions and instanton counting”, [ PDF: English, arXiv: math-ph/0601062 ]
  28. A. Okounkov, N. Reshetikhin, “The birth of a random matrix”, Mosc. Math. J., 6:3 (2006), 553–566.
  29. A. Okounkov, R. Pandharipande, "The local Donaldson-Thomas theory of curves", [ PDF: English, arXiv: math/0512573 ]
  30. R. Kenyon, A. Okounkov, “Limit shapes and the complex burgers equation”, [ PDF: English, arXiv: math-ph/0507007 ]
  31. A. Eskin, A. Okounkov, “Pillowcases and quasimodular forms”, [ PDF: English, arXiv: math/0505545 ]
  32. A. Okounkov, N. Reshetikhin, “Random skew plane partitions and the Pearcey process”, [ PDF: English, arXiv: math/0503508 ]
  33. A.M.Vershik, A.Yu.Okounkov, “A New Approach to the Representation Thoery of the Symmetric Groups. 2″, Zapiski Seminarod POMI (In Russian) v.307, 2004 [ PDF: English, arXiv: math/0503040 ] А. Вершик, А. Окуньков, “Новый подход к теории представлений симметрических групп. II”, Зап. научн. сем. ПОМИ, 307 (2004), 57–98.
  34. A. Okounkov, “Random surfaces enumerating algebraic curves”, [ PDF: English, arXiv: math-ph/0412008 ]
  35. A. Okounkov, R. Pandharipande, “Quantum cohomology of the Hilbert scheme of points in the plane”, [ PDF: English, arXiv: math/0411210 ]
  36. D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande, “Gromov-Witten theory and Donaldson-Thomas theory, II”, [ PDF: English, arXiv: math0406092 ]
  37. A. Eskin, A. Okounkov, R. Pandharipande, “The theta characteristic of a branched covering”, [ PDF: English, arXiv: math/0312186 ]
  38. D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande, “Gromov-Witten theory and Donaldson-Thomas theory, I”, [ PDF: English, arXiv: math/0312059 ]
  39. R. Kenyon, A. Okounkov, “Planar dimers and Harnack curves”, [ PDF: English, arXiv: math/0311062 ]
  40. R. Kenyon, A. Okounkov, S. Sheffield, “Dimers and Amoebae”, [ PDF: English, arXiv: math-ph/0311005 ]
  41. A. Okounkov, N. Reshetikhin, C. Vafa, “Quantum Calabi-Yau and Classical Crystals”, [ PDF: English, arXiv: hep-th/0309208 ]
  42. A. Okounkov, “Random trees and moduli of curves”, [ PDF: English, arXiv: math/0309075 ]
  43. A. Okounkov, “Symmetric functions and random partitions”, [ PDF: English, arXiv: math/0309074 ]
  44. A. Okounkov, “The uses of random partitions”, [ PDF: English, arXiv: math-ph/0309015 ]
  45. A. Okounkov, R. Pandharipande, “Virasoro constraints for target curves”,
    [ PDF: English, arXiv: math/0308097 ]
  46. A. Okounkov, R. Pandharipande, “Hodge integrals and invariants of the unknot”, Geom. Topol. 8 (2004) 675-699 [ PDF: English, arXiv: math/0307209 ]
  47. N. Nekrasov, A. Okounkov, “TSeiberg-Witten Theory and Random Partitions”, [ PDF: English, arXiv: hep-th/0306238 ]
  48. А. Окуньков, “Замечание о спаривании Фурье и биномиальной формуле для многочленов Макдональда”, Функц. анализ и его прил., 36:2 (2002), 62–68.
  49. A. Okounkov, R. Pandharipande, “The equivariant Gromov-Witten theory of P^1″, [ PDF: English, arXiv: math/0207233 ]
  50. E. Getzler, A. Okounkov, R. Pandharipande, “Multipoint series of Gromov-Witten invariants of CP^1″, [ PDF: English, arXiv: math/0207106 ]
  51. A. Okounkov, R. Pandharipande, “Gromov-Witten theory, Hurwitz theory, and completed cycles”, [ PDF: English, arXiv: math/0204305 ]
  52. A. Okounkov, “A remark on Fourier pairing and binomial formula for Macdonald polynomials”, [ PDF: English, arXiv: math/0110269 ]
  53. A. Okounkov, N. Reshetikhin, “Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram”, [ PDF: English, arXiv: math/0107056 ]
  54. A. Okounkov, “Generating functions for intersection numbers on moduli spaces of curves”, [ PDF: English, arXiv: math/0101201 ]
  55. A. Okounkov, R. Pandharipande, “Gromov-Witten theory, Hurwitz numbers, and Matrix models, I”, [ PDF: English, arXiv: math/0101147 ]
  56. A. Okounkov, “Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials”, [ PDF: English, arXiv: math/0008094 ]
  57. A. Eskin, A. Okounkov, “Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials”, [ PDF: English, arXiv: math/0006171 ]
  58. A. Okounkov, “Toda equations for Hurwitz numbers”, [ PDF: English, arXiv: math/0004128 ]
  59. A. Okounkov, “SL(2) and z-measures”, [ PDF: English, arXiv: math/0002135 ]
  60. A. Okounkov, “Why would multiplicities be log-concave ?”, [ PDF: English, arXiv: math/0002085 ]
  61. A. Borodin, A. Okounkov, “A Fredholm determinant formula for Toeplitz determinants”, [ PDF: English, arXiv: math/9907165 ]
  62. A. Okounkov, “Infinite wedge and random partitions”, [ PDF: English, arXiv: math/9907127 ]
  63. A. Borodin, A. Okounkov, G. Olshanski, “Asymptotics of Plancherel measures for symmetric groups”, J. Amer. Math. Soc. 13 (2000), no. 3, 481-515 [ PDF: English, arXiv: math/9905032 ]
  64. A. Okounkov, “Random Matrices and Random Permutations”, [ PDF: English, arXiv: math/9903176 ]
  65. A. Okounkov, “On the representations of the infinite symmetric group”, PhD thesis (1995) Записки научных семинаров POMI, 240 (1997), 167-230 [ PDF: English, arXiv: math/9803037 ]
  66. А. Окуньков, Г. Ольшанский, “Сдвинутые функции Шура”, Алгебра и анализ, 9:2 (1997), 73–146. “Shifted Schur Functions” [ PDF: English, arXiv: q-alg/9605042 ]
  67. А. Окуньков, “Замечание о полиноме Гильберта сферического многообразия”, Функц. анализ и его прил., 31:2 (1997), 82–85.
  68. А. Окуньков, “О представлениях бесконечной симметрической группы”, Зап. научн. сем. ПОМИ, 240 (1997), 166–228.
  69. A. Okounkov, “A characterization of interpolation Macdonald polynomials”, [ PDF: English, arXiv: q-alg/9712052 ]
  70. S. Bloch, A. Okounkov, “The Character of the Infinite Wedge Representation”, [ PDF: English, arXiv: alg-geom/9712009 ]
  71. A. Okounkov, G. Olshanski, “Asymptotics of Jack polynomials as the number of variables goes to infinity”, Intern. Math. Research Notices 1998, no. 13, 641-682 [ PDF: English, arXiv: q-alg/9709011 ]
  72. S. Kerov, A. Okounkov, G. Olshanski, “The boundary of Young graph with Jack edge multiplicities”, Intern. Math. Research Notices 1998, no. 4, 173-199. [ PDF: English, arXiv: q-alg/9703037 ]
  73. A. Okounkov, “On n-point correlations in the log-gas at rational temperature”, [ PDF: English, arXiv: hep-th/9702001 ]
  74. А. Вершик, А. Окуньков, “Индуктивный способ изложения теории представлений симметрических групп”, УМН, 51:2(308) (1996), 153–154.
  75. A. Okounkov, G. Olshanski, “Shifted Schur functions II. Binomial formula for characters of classical groups and applications”, In: Kirillov’s Seminar on Representation Theory. Amer. Math. Soc. Transl. 1998, pp. 245-271. [ PDF: English, arXiv: q-alg/9612025 ]
  76. A. Okounkov, “BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials”, [ PDF: English, arXiv: q-alg/9611011 ]
  77. A. Okounkov, “Binomial formula for Macdonald polynomials”, [ PDF: English, arXiv: q-alg/9608021 ]
  78. A. Okounkov, G. Olshanski, “Shifted Jack polynomials, binomial formula, and applications”, Math. Res. Letters, 4 (1997), 69-78 [ PDF: English, arXiv: q-alg/9608020 ]
  79. A. Okounkov, “(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formulas” [ PDF: English, arXiv: q-alg/9605013 ]
  80. A. Okounkov, “Quantum Immanants and Higher Capelli Identities”, Transformation Groups, 1 (1996), 99-126. [ PDF: English, arXiv: q-alg/9602028 ]
  81. A. Okounkov, “Young Basis, Wick Formula, and Higher Capelli Identities”, Internat. Math. Res. Notices, 17 (1996), 817-839. [ PDF: English, arXiv: q-alg/9602027 ]
  82. А. Окуньков, “Ручные представления алгебры Гекке H(∞)H(∞) и qq-аналоги частичных биекций”, Зап. научн. сем. ПОМИ, 223 (1995), 92–107.
  83. А. Окуньков, “Теорема Тома и представления бесконечной бисимметрической группы”, Функц. анализ и его прил., 28:2 (1994), 31–40.
  84. А. Окуньков, “О представлении орбит в виде суммы элементарных орбит”, УМН, 49:4(298) (1994), 147–148.