Михаил Финкельберг

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

Профессиональные интересы:
алгебраическая геометрия, теория представлений

Публикации

  1. M. Finkelberg, R. Fujita, “Coherent IC-sheaves on type An affine Grassmannians and dual canonical basis of affine type A1″, [ PDF: English, arXiv: 1901.05994 ]
  2. A. Braverman, M. Finkelberg, “A quasi-coherent description of the the category of D-mod(GrGL(n))”, [ PDF: English, arXiv: 1809.10774 ]
  3. A. Braverman, M. Finkelberg, “Coulomb branches of 3-dimensional gauge theories and related structures”, [ PDF: English, arXiv: 1807.09038 ]
  4. A. Braverman, M. Finkelberg, H. Nakajima, “Line bundles over Coulomb branches”, [ PDF: English, arXiv: 1805.11826 ]
  5. M. Finkelberg, V. Krylov, I. Mirković, “Drinfeld-Gaitsgory interpolation Grassmannian and geometric Satake equivalence (with appendix by D. Gaitsgory)”, [ PDF: English, arXiv: 1805.07721 ]
  6. M. Finkelberg, J. Kamnitzer, K. Pham, L. Rybnikov, A. Weekes, “Comultiplication for shifted Yangians and quantum open Toda lattice”, Adv. Math. 327(2018)349-389
  7. M. Finkelberg, A. Ionov, “Kostka-Shoji polynomials and Lusztig’s convolution diagram”, Inst. Math. Acad. Sinica, 13:1 (2018) 31-42
  8. M. Finkelberg, A. Kuznetsov, L. Rybnikov, G. Dobrovolska, “Towards a cluster structure on trigonometric zastava”, Sel. Math. New Ser. (2018) 24:1 187-225
  9. M. Finkelberg, A. Tsymbaliuk, “Multiplicative slices, relativistic Toda and shifted quantum affine algebras”, [ PDF: English, arXiv: 1708.01795 ]
  10. A. Braverman, M. Finkelberg, H. Nakajima, “Ring objects in the equivariant derived Satake category arising from Coulomb branches”, [ PDF: English, arXiv: 1706.02112 ]
  11. A. Braverman, P. Etingof, M. Finkelberg, “Cyclotomic double affine Hecke algebras (with an appendix by Hiraku Nakajima and Daisuke Yamakawa)”, [ PDF: English, arXiv: 1611.10216 ]
  12. A. Braverman, M. V. Finkelberg, H. Nakajima, “Instanton moduli spaces and V-Algebras”, Asterisque. 2017
  13. A. Braverman, M. V. Finkelberg, Nakajima H., “Coulomb branches of 3d N=4 quiver gauge theories and slices in the affine Grassmannian”, [ PDF: English, arXiv: 1604.03625 ]
  14. A. Braverman, G. Dobrovolska, M. V. Finkelberg, “Gaiotto–Witten superpotential and Whittaker D-modules on monopoles”, Adv. in Mathematics. 2016. Vol. 300. P. 451-472. [ PDF: English, arXiv: 1406.6671 ]
  15. M. V. Finkelberg, “Geometry and combinatorics of Kostka-Shoji polynomials”, in: Oberwolfach reports Vol. 13. Issue 1. Zürich : European Mathematical Society Publishing house, 2016. P. 628-629.
  16. A. Braverman, M. Finkelberg, H. Nakajima, “Instanton moduli spaces and W-algebras”, Astérisque No. 385 (2016), vii+128 pp. [ PDF: English, arXiv: 1406.2381v5 ]
  17. M. Finkelberg, V. Ginzburg, A. Ionov, A. Kuznetsov, “Intersection cohomology of the Uhlenbeck compactification of the Calogero-Moser space”, Selecta Mathematica, New Series. 2016. Vol. 22. No. 4. P. 2491-2534. [ PDF: English, arXiv: 1506.05205 ]
  18. M. Finkelberg, A. Ionov, “Kostka-Shoji polynomials and Lusztig’s convolution diagram”, [ arXiv: 1605.05806, PDF: English ]
  19. M. V. Finkelberg, R. Bezrukavnikov, A. Braverman, D. Gaitsgory, “The Mathematics of Joseph Bernstein”, Selecta Mathematica, New Series. 2016. Vol. 22. No. 4. P. 1793-1795.
  20. M. Finkelberg, A. Kuznetsov, L. Rybnikov, G. Dobrovolska, “Towards a cluster structure on trigonometric zastava”, Selecta Math. (N.S.), 2016, 1–39. [ PDF: English, arXiv: 1504.05605 ].
  21. A. Braverman, M. Finkelberg, H. Nakajima, “Towards a mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories”, II. [ PDF: English, arXiv: 1601.03586 ]
  22. Д. В. Кубрак, М. В. Финкельберг, “Исчезающие циклы на пуассоновых многообразиях”, Функц. анализ и его прил., 49:2 (2015), 70–78; Funct. Anal. Appl., 49:2 (2015), 135–141. [ PDF: English, arXiv: 1212.3051 ]
  23. E. Feigin, M. V. Finkelberg, M. Reineke, “Degenerate affine Grassmannians and loop quivers”, Kyoto J. Math. 57:2 (2017), 445-474. [ PDF: English, arXiv: 1410.0777 ]
  24. A. Braverman, M. Finkelberg, J. Shiraishi, “Macdonald polynomials, Laumon spaces and perverse coherent sheaves”, in: Contemporary Mathematics / Eds.: P. Etingof, M. Khovanov, A. Savage. Vol. 610: Perspectives in Representation Theory. New Haven : Yale University Press, 2014. P. 23-41. [ PDF: English, arXiv: 1206.3131 ]
  25. M. Finkelberg, V. Schechtman, “Microlocal approach to Lusztig’s symmetries”, [ PDF: English, arXiv: 1401.5885 ]
  26. M. Finkelberg, L. Rybnikov, “Quantization of Drinfeld Zastava in type A”, J. of the European Mathematical Society. 2014. Vol. 16. No. 2. P. 235-271. [ PDF: English, arXiv: 1009.0676 ]
  27. M. Finkelberg, L. Rybnikov, “Quantization of Drinfeld Zastava in type С”, Algebraic Geometry. 2014. Vol. 1. No. 2. P. 166-180. [ PDF: English, arXiv: 1306.5427 ]
  28. A. Braverman, M. Finkelberg, “Semi-infinite Schubert varieties and quantum K-theory of flag manifolds”, // Journal of the American Mathematical Society. 2014. Vol. 27. No. 4. P. 1147-1168. [ PDF: English, arXiv: 1111.2266 ]
  29. E. Feigin, M. Finkelberg, P. Littelmann, “Symplectic Degenerate Flag Varieties”, Canadian Journal of Mathematics. 2014. Vol. 66. No. 6. P. 1250-1286. [ PDF: English, arXiv: 1106.1399 ]
  30. A. Braverman, M. Finkelberg, “Twisted zastava and q-Whittaker functions”, J. London Math. Soc. (2) 96 (2017) 309-325. [ PDF: English, arXiv: 1410.2365 ]
  31. M. Finkelberg, A. Braverman, “Weyl modules and q-Whittaker functions”, Math. Ann. 359 (2014), no.1-2, 45-59. [ PDF: English, arXiv: 1203.1583 ]
  32. R. Bezrukavnikov, M. Finkelberg, “Wreath Macdonald polynomials and the categorical McKay correspondence”, Cambridge J. of Mathematics. 2014. Vol. 2. No. 2. P. 163-190. [ PDF: English, arXiv: 1208.3696 ]
  33. 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.
  34. M. Finkelberg, “Laumon spaces”, Пер. с англ., Mathematical Sciences. 2013. Vol. 51. No. 596. P. 46-51.
  35. A. Braverman, M. Finkelberg, “Pursuing the double affine Grassmannian III: convolution with affine zastava”, Mosc. Math. J., 13:2 (2013), 233–265. [ PDF: English, arXiv: 1010.3499 ]
  36. A. Braverman, M. Finkelberg, D. Kazhdan, “Affine Gindikin-Karpelevich Formula via Uhlenbeck Spaces”, Springer Proceedings in Mathematics & Statistics. 2012. Vol. 9. P. 17-29. [ PDF: English, arXiv: 0912.5132 ]
  37. R. Bezrukavnikov, M. Finkelberg, V. Ostrik, “Character D-modules via Drinfeld center of Harish-Chandra bimodules”, Inventiones Mathematicae. 2012. Vol. 188. No. 3. P. 589-620. [ PDF: English, arXiv: 0902.1493 ]
  38. M. Finkelberg, A. Braverman, “Pursuing the double affine Grassmannian II. Convolution”, Advances in Mathematics. 2012. No. 230. P. 414-432. [ PDF: English, arXiv: 0908.3390 ]
  39. A. Braverman, B. Feigin, L. Rybnikov, M. Finkelberg, “A finite analog of the AGT relation I: finite W-algebras and quasimaps’ spaces”, Communications in Mathematical Physics, Vol. 308, Number 2, 457-478 (2011). [ PDF: English, arXiv: 1008.3655]
  40. A. Braverman, M. Finkelberg, “Dynamical Weyl groups and equivariant cohomology of transversal slices on affine Grassmannians”, Mathematical Research Lett., Vol. 18, N 3, 2011, pp. 505-512. [ PDF: English, arXiv: 1010.2135 ]
  41. B. Feigin, M. Finkelberg, I. Frenkel, L. Rybnikov, “Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces”, Selecta Mathematica, New Series. 2011. Vol. 17. No. 2. P. 337-361. [ PDF: English, arXiv: 0806.0072 ]
  42. B. Feigin, M. Finkelberg, A. Negut, L. Rybnikov, “Yangians and cohomology rings of Laumon spaces”, Selecta Mathematica, New Series. 2011. Vol. 17. No. 3. P. 573-607. [ PDF: English, arXiv: 0812.4656 ]
  43. M. Finkelberg, V. Ginzburg, “Cherednik algebras for algebraic curves”, Progress in Mathematics. 2010. No. 284. P. 121-153. [ PDF: English, arXiv: 0704.3494 ]
  44. M. Finkelberg, V. Ginzburg, “On mirabolic D-modules”, International Mathematics Research Notices. 2010. No. 15. pp. 2947-2986. [ PDF: English, arXiv: 0803.0578 ]
  45. A. Braverman, M. Finkelberg, “Pursuing the double affine Grassmannian I: Transversal slices via instantons on A_k-singularities”, Duke Mathematical J. 2010. Vol. 152. No. 1. P. 175-206. [ PDF: English, arXiv: 0711.2083 ]
  46. M. Finkelberg, S. Lysenko, “Twisted geometric Satake equivalence:, J. of the Institute of Mathematics Jussieu. 2010. Vol. 9. No. 4. pp. 719-739. [ PDF: English, arXiv: 0809.3738 ]
  47. M. Finkelberg, V. Ginzburg, R. Travkin, “Mirabolic affine Grassmannian and character sheaves”, Selecta Mathematica, New Series. 2009. Vol. 14. No. 3-4. pp. 607-628. [ PDF: English, arXiv: 0802.1652 ]
  48. R. Bezrukavnikov, M. Finkelberg, “Equivariant Satake category and Kostant–Whittaker reduction”, Mosc. Math. J., 8:1 (2008), 39–72. [ PDF: English, arXiv: 0707.3799 ]
  49. R. Bezrukavnikov, M. Finkelberg, V.Ginzburg, “Cherednik algebras and Hilbert schemes in characteristic p, Electronic Representation Theory 10 (2006), 254-298. [ PDF: English, arXiv: math/0312474 ]
  50. A.Braverman, M.Finkelberg, D.Gaitsgory, “Uhlenbeck spaces via affine Lie algebras, Progress in Mathematics 244 (2006), 17-135. [ PDF: English, arXiv: math/0301176 ]
  51. R. Bezrukavnikov, M. Finkelberg, I. Mirkovic, “Equivariant homology and K-theory of affine Grassmannians and Toda latice”, Compositio Mathematica. 2005. Vol. 141. No. 3. pp. 746-768. [ PDF: English, arXiv: math/0306413 ]
  52. A. Braverman, M. Finkelberg, “Finite difference quantum Toda lattice via equivariant K-theory”, Transformation Groups. 2005. Vol. 10. No. 3-4. pp. 1-23. [ PDF: English, arXiv: 0503456 ]
  53. M. Finkelberg, D. Gaitsgory, A. Kuznetsov, “Uhlenbeck spaces for A2 and affine Lie algebra sln“, Publ. Res. Inst. Math. Sci. 39:4 (2003), 721-766. [ PDF: English, arXiv: math/0202208 ]
  54. A. Braverman, D. Gaitsgory, M. Finkelberg, I.Mirkovic, “Intersection cohomology of Drinfeld’s compactifications”, Selecta Math. (N.S.) 8:3 (2002), 381-418. [ PDF: English, arXiv: math/0012129 ]
  55. M. Finkelberg, V. Ginzburg, “Calogero-Moser space and Kostka polynomials”, Adv. Math. 172:1 (2002), 137-150. [ PDF: English, arXiv: math/0110190 ]
  56. M. Finkelberg, A. Kuznetsov, “Parabolic sheaves on surfaces and affine Lie algebra, J. Reine Angew. Math. 529 (2000), 155-203. [ PDF: English, arXiv: math/9903181 ]
  57. B. Feigin, M. Finkelberg, A. Kuznetsov, I. Mirkovic, “Semi-infinite flags. II. Local and global intersection cohomology of quasimaps’ spaces”, Amer. Math. Soc. Transl. Ser. 2, vol. 194 (1999), 113-148. [ PDF: English, arXiv: alg-geom/9711009 ]
  58. M. Finkelberg, I. Mirkovic, “Semi-infinite flags. I. Case of global curve P1“, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc, Providence, RI (1999), 81-112. [ PDF: English, arXiv: alg-geom/9707010 ]
  59. M. Finkelberg, A. Kuznetsov, N. Markarian, I. Mirkovic, “A note on a symplectic structure on the space of G-monopoles”, Comm. Math. Phys. 201:2 (1999), 411-421. [ PDF: English, arXiv: math/9803124 ]
  60. R. Bezrukavnikov, M. Finkelberg, V. Schechtman, “Factorizable sheaves and quantum groups”, Lecture Notes in Mathematics. 1998. Vol. 1691. Springer Verlag, Berlin. [ PDF: English, arXiv: q-alg/9712001 ]
  61. M. Finkelberg, A. Kuznetsov, I. Mirkovic, “The singular supports of 1С sheaves on spaces of quasimaps are irreducible”, Amer. Math. Soc. Transl. Ser. 2, 185, Amer. Math. Soc, Providence, RI (1998), 85-93. [ PDF: English, arXiv: alg-geom/9705003 ]
  62. M. Finkelberg, A. Kuznetsov, “Global intersection co-homology of quasimaps’ spaces”, Internat. Math. Res. Notices 1997, no. 7, 301-328. [ PDF: English, arXiv: alg-geom/9702010 ]
  63. M. Finkelberg, “An equivalence of fusion categories”, Geom. Funct. Anal. 6:2 (1996), 249-267.
  64. М. Финкельберг, В. Шехтман, “Локализация модулей над небольшими квантовыми группами”, Алгебраическая геометрия – 5, Итоги науки и техн. Сер. Соврем. мат. и ее прил. Темат. обз., 34, ВИНИТИ, М., 2001, 5–66; J. Math. Sci., 82:1 (1996), 3127–3164.
  65. М. В. Финкельберг, “Ортогональный индекс Маслова”, Функц. анализ и его прил., 29:1 (1995), 92–95; Funct. Anal. Appl., 29:1 (1995), 72–74.
  66. A. Vishik, M. Finkelberg, “The coordinate ring of general curve of genus g > 5 is Koszul”, J. of Algebra. 1993. Vol. 162. No. 2. P. 535-539.
  67. V. Lunts, M. Finkelberg, P. Bressler, “Vanishing cycles on Grassmannians”, Duke Math. J. 61:3 (1990), 763-777.