Евгений Фейгин

профессор / Сколковский институт науки и технологий
профессор / Национальный исследовательский университет “Высшая школа экономики” / факультет математики

Профессиональные интересы
теория представлений, математическая физика, алгебраическая геометрия, комбинаторика

Образование, учёные степени
2002 / Независимый Московский университет, математический факультет
2002 / Московский государственный университет, механико-математический факультет
2005 / Кандидат физико-математических наук / Московский государственный университет/ специальность 01.01.06 “Математическая логика, алгебра и теория чисел” / тема диссертации: “Модули Демазюра для аффинной алгебры Ли sl(2)”
2013 / Доктор физико-математических наук / Институт проблем передачи информации им. А.А.Харкевича РАН / специальность 01.01.06 “Математическая логика, алгебра и теория чисел” / тема диссертации: “Вырождение Пуанкаре-Биркгофа-Витта в теории Ли и его приложения”

Публикации

  1. E. Feigin, “Tensor products, Kerov’s theorem and GUE eigenvalues density” [ PDF: English, arXiv: 1902.01154]
  2. G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier, M. Reineke, “Linear degenerations of flag varieties: partial flags, defining equations, and group actions” [ PDF: English, arXiv: 1901.11020]
  3. E. Feigin, I. Makedonskyi, D. Orr, “Generalized Weyl modules and nonsymmetric q-Whittaker functions”, Adv. Math. (2018) 330 997-1033 [ PDF: English, arXiv: 1605.01560 ]
  4. A. Bigeni, E. Feigin, “Symmetric Dellac configurations”, [ PDF: English, arXiv: 1808.04275 ]
  5. A. Bigeni, E. Feigin, “Poincaré polynomials of the degenerate flag varieties of type C”, [ PDF: English, arXiv: 1804.10804 ]
  6. E. Feigin, I. Makedonskyi, “Vertex algebras and coordinate rings of semi-infinite flags, Feigin, E. & Makedonskyi, I. Commun. Math. Phys. (2019), doi.org/10.1007/s00220-019-03321-x [ PDF: English, arXiv: 1804.03359 ]
  7. X. Fang, E. Feigin, G. Fourier, I. Makhlin, “Weighted PBW degenerations and tropical flag varieties”, [ PDF: English, arXiv: 1711.00751]
  8. E. Feigin, I. Makedonskyi, “Semi-infinite Plücker relations and Weyl modules”, [ PDF: English, arXiv: 1709.05674]
  9. E. Feigin, I. Makedonskyi, “Weyl modules for osp(1,2) and nonsymmetric Macdonald polynomials”, Math.Res.Lett., 24(3), (2017), 741–766
  10. Е. А. Македонский, Е. Б. Фейгин, “Обобщенные модули Вейля для скрученных алгебр токов”, ТМФ, 192:2 (2017), 284–306; Theoret. and Math. Phys., 192:2 (2017), 1184–1204, [ PDF: English, arXiv: 1606.05219 ]
  11. E. Feigin, S. Kato, I. Makedonskyi, “Representation theoretic realization of non-symmetric Macdonald polynomials at infinity”, [ PDF: English, arXiv: 1703.04108 ]
  12. Е. Б. Фейгин, “ПБВ-вырождение: алгебра, геометрия и комбинаторика”, Труды семинара по алгебре и геометрии Самарского университета, Итоги науки и техн. Сер. Соврем. мат. и ее прил. Темат. обз., 136, ВИНИТИ РАН, Москва, 2017, 3–30
  13. G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier, M. Reineke, “Linear degenerations of flag varieties”, Mathematische Zeitschrift, (2017) 287:615–654, [ PDF: English, arXiv: 1603.08395 ]
  14. E. Feigin, I. Makhlin, “Vertices of FFLV polytopes”, [ PDF: English, arXiv: 1604.08844 ]
  15. G. Cerulli Irelli, E. Feigin, M. Reineke, “Schubert Quiver Grassmannians”, [ PDF: English, arXiv: 1508.00264 ]
  16. I. Cherednik, E. Feigin, “Extremal part of the PBW-filtration and nonsymmetric Macdonald polynomials”, Advances in Mathematics. 2015. Vol. 282. P. 220-264. [ PDF: English, arXiv: 1407.6316 ]
  17. E. Feigin, I. Makedonskyi, “Generalized Weyl modules, alcove paths and Macdonald polynomials”, Sel. Math. New Ser. (2017) 23: 2863 [ PDF: English, arXiv: 1512.03254 ]
  18. E. Feigin, I. Makedonskyi, “Nonsymmetric Macdonald polynomials and PBW filtration: towards the proof of the Cherednik-Orr conjecture”, J. of Combinatorial Theory, Series A. 2015. P. 60-84.
  19. E. Feigin, I. Makedonskyi, “Weyl modules for osp(1,2) and nonsymmetric Macdonald polynomials”, [ PDF: English, arXiv: 1507.01362 ].
  20. E. Feigin, M. Finkelberg, M. Reineke, “Degenerate affine Grassmannians and loop quivers”, Kyoto J. Math. 57:2 (2017), 445-474. [ PDF: English, arXiv: 1410.0777]
  21. Е. Б. Фейгин, “Вырожденная группа типа A: представления и многообразия флагов”, Функц. анализ и его прил., 48:1 (2014), 73–88; Funct. Anal. Appl., 48:1 (2014), 59–71.
  22. G. Cerulli Irelli, E. Feigin, M. Reineke, “Homological approach to the Hernandez-Leclerc construction and quiver varieties”, Representation Theory. 2014. No. 18. P. 1-14. [ PDF: English, arXiv: 1302.5297 ]
  23. E. Feigin, M. Finkelberg, P. Littelmann, “Symplectic Degenerate Flag Varieties”, Canadian J. of Mathematics. 2014. Vol. 66. No. 6. P. 1250-1286. [ PDF: English, arXiv: 1106.1399 ]
  24. E. Feigin, M. Finkelberg, “Degenerate flag varieties of type A: Frobenius splitting and BW theorem”, Mathematische Zeitschrift. 2013. Vol. 275. No. 1-2. P. 55-77. [ PDF: English, arXiv: 1103.1491 ]
  25. G. Cerulli Irelli, E. Feigin, M. Reineke, “Degenerate flag varieties: moment graphs and Schröder numbers”, Journal of Algebraic Combinatorics. 2013. Vol. 38. No. 1. P. 159-189. [ PDF: English, arXiv: 1206.4178 ]
  26. G. Cerulli Irelli, E. Feigin, M. Reineke, “Desingularization of quiver Grassmannians for Dynkin quivers”, Advances in Mathematics. 2013. No. 245. P. 182-207. [ PDF: English, arXiv: 1209.3960 ]
  27. E. Feigin, G. Fourier, P. Littelmann, “Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations”, [ PDF: English, arXiv: 1306.1292 ]
  28. E. Feigin, G. Fourier, P. Littelmann, “PBW-filtration over ℤ and Compatible Bases for V_Z(\lambda) in Type A_n and C_n”, in: Symmetries, Integrable Systems and Representations Vol. 40: Symmetries, Integrable Systems and Representations. Springer, 2013. P. 35-63. [ PDF: English, arXiv: 1204.1854 ]
  29. E. Feigin, “GaM degeneration of flag varieties”, Selecta Mathematica, New Series. 2012. Vol. 18. No. 3. pp. 513-537. [ PDF: English, arXiv: 1007.0646 ]
  30. G. Cerulli Irelli, E. Feigin, M. Reineke, “Quiver Grassmannians and degenerate flag varieties”, Algebra & Number Theory. 2012. Vol. 6. No. 1. pp. 165-194. [ PDF: English, arXiv: 1106.2399 ]
  31. Е. Б. Фейгин, “Системы корреляционных функций, коинварианты и алгебра Верлинде”, Функц. анализ и его прил., 46:1 (2012), 49–64. [ PDF: English, arXiv: 1003.2949 ]
  32. E. Feigin, “The median Genocchi numbers, q-analogues and continued Fractions”, European J. of Combinatorics. 2012. Vol. 33. No. 1. P. 1913-1918. [ PDF: English, arXiv: 1111.0740 ]
  33. E. Feigin, “Degenerate flag varieties and the median Genocchi numbers”, Mathematical Research Letters. 2011. No. 18(6). pp. 1-16. [ PDF: English, arXiv: 1101.1898 ]
  34. E. Feigin, G. Fourier, P. Littelmann, “PBW filtration and bases for irreducible modules in type An“, Transformation Groups. 2011. Vol. 16. No. 1. P. 71-89. [ PDF: English, arXiv: 1002.0674 ]
  35. E. Feigin, G. Fourier, P. Littelmann, “PBW filtration and bases for symplectic Lie algebras”, International Mathematics Research Notices. 2011. Vol. 2011. No. 24. P. 5760-5784. [ PDF: English, arXiv: 1010.2321 ]
  36. B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Quantum continuous gl∞: Tensor products of Fock modules and Wn-characters”, J. of Mathematics of Kyoto University. 2011. Vol. 51. No. 2. P. 365-392. [ PDF: English, arXiv: 1002.3113 ]
  37. B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Quantum continuous gl∞: semiinfinite construction of representations”, J. of Mathematics of Kyoto University. 2011. Vol. 51. No. 2. P. 337-364. [ PDF: English, arXiv: 1002.3100 ]
  38. B. Feigin, E. Feigin, P. Littelmann, “Zhu’s algebras, C_2-algebras and abelian radicals”, J. of Algebra. 2011. Vol. 329. P. 130-146. [ PDF: English, arXiv: 0907.3962 ]
  39. E. Feigin, J. van de Leur, S. Shadrin, “Givental symmetries of Frobenius manifolds and multi-component KP tau-functions”, Adv. Math. 224 (2010), no. 3, 1031-1056. [ PDF: English, arXiv: 0905.0795 ]
  40. E. Feigin, P. Littelmann, “Zhu’s algebra and the $C_2$-algebra in the symplectic and the orthogonal cases”, J. of Physics A: Mathematical and Theoretical. 2010. Vol. 43. No. 13. [ PDF: English, arXiv: 0911.2957 ]
  41. E. Feigin, “N=1 formal genus 0 Gromov-Witten theories and Givental’s formalism”, J.Geom.Phys.59:1127-1136,2009. [ PDF: English, arXiv: 0803.3554 ]
  42. B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Principal sl(3) subspaces and quantum Toda Hamiltonian”, Advances in Pure Mathematics 54, Algebraic Analysis and Around, (2009) 109-166
  43. B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, “Fermionic Formulas for Eigenfunctions of the Difference Toda Hamiltonian”, Letters in Mathematical Physics. 2009. Vol. 88. No. 1-3. P. 39-77. [ PDF: English, arXiv: 0812.2306 ]
  44. B. Feigin, E. Feigin, I. Tipunin, “Fermionic formulas for (1,p) logarithmic model characters in Ф2,1 quasi¬particle realization”, Advanced Studies in Pure Mathematics 61, 161-184 (2011)
  45. E. Feigin, “The PBW filtration”, Representation Theory. 2009. No. 13. P. 165-181.
  46. B. Feigin, E. Feigin, M. Jimbo, T. Miwa, Y. Takeyama, “A φ {1,3}-filtration of the Virasoro minimal series M(p,p’) with 1 < p'/p < 2", Publications of the Research Institute for Mathematical Sciences. 2008. Vol. 44. No. 2. P. 213-257. [ PDF: English, arXiv: math/0603070 ]
  47. Е. Б. Фейгин, “Бозонные формулы для аффинных функций ветвления”, Функц. анализ и его прил., 42:1 (2008), 63–77; Funct. Anal. Appl., 42:1 (2008), 53–64. [ PDF: English, arXiv: math/0604370 ]
  48. E. Feigin, “The PBW Filtration, Demazure Modules and Toroidal Current Algebras”, SIGMA, 4 (2008), 070, 21 pp. [ PDF: English, arXiv: 0806.4851 ]
  49. E. Feigin, “Infinite fusion products and $\hat{\mathfrak{sl}_2}$ cosets”, J. of Lie Theory. 2007. Vol. 17. pp. 145-161. [ PDF: English, arXiv: math/0603226 ]
  50. B. Feigin, E. Feigin, “Two-dimensional current algebras and affine fusion product”, J. of Algebra. 2007. Vol. 313. No. 1. pp. 176-198. [ PDF: English, arXiv: math/0607091 ]
  51. B. Feigin, E. Feigin, “Principal subspace for the bosonic vertex operator $\phi\sb {\sqrt{2m}}(z)$ and Jack polynomials”, Advances in Mathematics. 2006. Vol. 206 . No. 2. P. 307-328. [ PDF: English, arXiv: math/0407372 ]
  52. B. Feigin, E. Feigin, “Homological realization of restricted Kostka polynomials”, International Mathematics Research Notices. 2005. Vol. 33. No. 33. P. 1997-2029. [ PDF: English, arXiv: math/0503058 ]
  53. B. Feigin, E. Feigin, “Schubert varieties and the fusion products”, Publications of the Research Institute for Mathematical Sciences. 2004. Vol. 40. No. 3. P. 625-668. [ PDF: English, arXiv: math/0305437 ]
  54. E. Feigin, “Schubert varieties and the fusion products: the general case”, Int. Math. Res. Not. 2004, no. 59, 3153-3175
  55. B. Feigin, E. Feigin, “Integrable sl2-modules as infinite tensor products”, Fundamental mathematics today, O. Sheinman, S. Lando eds., 304-334, Independent University of Moscow, 2003 (in Russian)
  56. B. Feigin, E. Feigin, “Q-characters of the tensor products in sl2-case”, Mosc. Math. J., 2:3 (2002), 567–588. [ PDF: English, arXiv: math/0201111 ]