Александр Браверман

приглашенный профессор / Сколковский институт науки и технологий
профессор / Торонтский университет

Профессиональные интересы:
геометрическая теория представлений (с приложениями к алгебраической геометрии, теории чисел и математической физике).

Образование, учёные степени
1993 / BSc / Тель-Авивский университет
1998 / PhD / Тель-Авивский университет


  1. A. Braverman, M. Finkelberg, “A quasi-coherent description of the the category of D-mod(GrGL(n))”, [ PDF: English, arXiv: 1809.10774 ]
  2. A. Braverman, M. Finkelberg, “Coulomb branches of 3-dimensional gauge theories and related structures”, [ PDF: English, arXiv: 1807.09038 ]
  3. A. Braverman, M. Finkelberg, H. Nakajima, “Line bundles over Coulomb branches”, [ PDF: English, arXiv: 1805.11826 ]
  4. A. Braverman, D. Kazhdan, “Schwartz space of parabolic basic affine space and asymptotic Hecke algebras”, [ PDF: English, arXiv: 1804.00336 ]
  5. A. Braverman, M. Finkelberg, H. Nakajima, “Ring objects in the equivariant derived Satake category arising from Coulomb branches”, [ PDF: English, arXiv: 1706.02112 ]
  6. A. Braverman, D. Kazhdan, “Remarks on the asymptotic Hecke algebra “, [ PDF: English, arXiv: 1704.03019 ]
  7. 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 ]
  8. A. Braverman, M. V. Finkelberg, H. Nakajima, “Instanton moduli spaces and V-Algebras”, Asterisque. 2017
  9. 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 ]
  10. 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 ]
  11. A. Braverman, M. Finkelberg, H. Nakajima, “Instanton moduli spaces and W-algebras”, Astérisque No. 385 (2016), vii+128 pp. [ PDF: English, arXiv: 1406.2381v5 ]
  12. A. Braverman, M. Finkelberg, H. Nakajima, “Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories, II”, [ PDF: English, arXiv: 1601.03586 ]
  13. 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.
  14. A. Braverman, D. Kazhdan, R. Bezrukavnikov, “Bernstein components via Bernstein center”, [ PDF: English, arXiv: 1512.08637 ]
  15. 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 ]
  16. 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 ]
  17. A. Braverman, M. Finkelberg, “Twisted zastava and q-Whittaker functions”, [ PDF: English, arXiv: 1410.2365 ]
  18. A. Braverman, D. Kazhdan, M. Patnaik, “Iwahori-Hecke algebras for p-adic loop groups”, [ PDF: English, arXiv: 1403.0602 ]
  19. A. Braverman, D. Kazhdan, “Cartan decomposition for complex loop groups”, [ PDF: English, arXiv: 1402.1369 ]
  20. A. Braverman, H. Garland, D. Kazhdan, M. Patnaik, “An affine Gindikin-Karpelevich formula”, [ PDF: English, arXiv: 1212.6473]
  21. M. Finkelberg, A. Braverman, “Weyl modules and q-Whittaker functions”, Math. Ann. 359 (2014), no.1-2, 45-59. [ PDF: English, arXiv: 1203.1583 ]
  22. A. Braverman, D. Kazhdan, “Representations of affine Kac-Moody groups over local and global fields: a survey of some recent results”, [ PDF: English, arXiv: 1205.0870 ]
  23. 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 ]
  24. 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 ]
  25. 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 ]
  26. 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]
  27. 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 ]
  28. A. Braverman, D. Maulik, A. Okounkov, “Quantum cohomology of the Springer resolution”, [ PDF: English, arXiv: 1001.0056 ]
  29. Alexander Braverman, David Kazhdan, “The spherical Hecke algebra for affine Kac-Moody groups I”, [ PDF: English, arXiv: 0809.1461 ]
  30. 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 ]
  31. A. Braverman, M. Finkelberg, D. Gaitsgory, “Uhlenbeck spaces via affine Lie algebras, Progress in Mathematics 244 (2006), 17-135. [ PDF: English, arXiv: math/0301176 ]
  32. A. Braverman, D. Gaitsgory ,”Deformations of local systems and Eisenstein series”, [ PDF: English, arXiv: math/0605139 ]
  33. A. Braverman, ” Spaces of quasi-maps into the flag varieties and their applications”, [ PDF: English, arXiv: math/0603454 ]
  34. R. Bezrukavnikov, A. Braverman, “Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case”, Pure Appl. Math. Q. 3 (2007), no. 1, Special Issue: In honor of Robert D. MacPherson. Part 3, 153-179. [ PDF: English, arXiv: math/0602255 ]
  35. A. Braverman, D. Kazhdan, “Some examples of Hecke algebras over 2-dimensional local fields”, [ PDF: English, arXiv: math/0510538 ]
  36. S. Arkhipov, R. Bezrukavnikov, A. Braverman, D. Gaitsgory, I. Mirkovic, ” Modules over the small quantum group and semi-infinite flag manifold”, [ PDF: English, arXiv: math/0505280 ]
  37. 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 ]
  38. A. Braverman, D. Gaitsgory, M. Vybornov, “Relation between two geometrically defined bases in representations of $GL_n$”, [ PDF: English, arXiv: 0411252 ]
  39. A. Braverman, P. Etingof, “Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential”, [ PDF: English, arXiv: 0409441 ]
  40. A. Braverman, “Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors”, [ PDF: English, arXiv: 0401409 ]
  41. 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 ]
  42. R. Bezrukavnikov, A. Braverman, I. Mirkovic, “Some results about the geometric Whittaker model”, [ PDF: English, arXiv: math/0210250 ]
  43. A. Braverman, D. Kazhdan, “Normalized intertwining operators and nilpotent elements in the Langlands dual group”, [ PDF: English, arXiv: math/0206119 ]
  44. A. Braverman, ” On Euler Characteristic of equivariant sheaves”, [ PDF: English, arXiv: math/0202165 ]
  45. A. Braverman, D. Kazhdan, “Gamma sheaves on reductive groups”, [ PDF: English, arXiv: math/0109033 ]
  46. R. Bezrukavnikov, A. Braverman, L. Positselskii, “Gluing of abelian categories and differential operators on the basic affine space”, Journ. Inst. Math. Jussieu 1 #4 (2002) 543-557. [ PDF: English, arXiv: math/0104114 ]
  47. A. Braverman, D. Gaitsgory, M. Finkelberg, I. Mirkovic, “Intersection cohomology of Drinfeld’s compactifications”, [ PDF: English, arXiv: math/0012129 ]
  48. A. Braverman, D. Kazhdan, V. Vologodsky, “Gamma-functions of representations and lifting”, [ PDF: English, arXiv: math/9912208 ]
  49. A. Braverman, D. Gaitsgory, “Geometric Eisenstein series”, [ PDF: English, arXiv: math/9912097 ]
  50. A. Braverman, D. Gaitsgory, “Crystals via the affine Grassmannian”, [ PDF: English, arXiv: math/9909077 ]
  51. A. Braverman, D. Gaitsgory, “On Ginzburg’s Lagrangian construction of representations of GL(n)”, [ PDF: English, arXiv: math/9901056 ]
  52. A. Braverman, A. Polishchuk, “Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formula”, [ PDF: English, arXiv: math/9810006 ]
  53. A. Braverman, D. Kazhdan, “On the Schwartz space of the basic affine space”, [ PDF: English, arXiv: math/9809112 ]
  54. A. Braverman, M. Braverman, “Tempered currents and the cohomology of the remote fiber of a real polynomial map”, [ PDF: English, arXiv: alg-geom/9704001 ]
  55. A. Braverman, P. Etingof, D. Gaitsgory, “Quantum integrable systems and differential Galois theory”, [ PDF: English, arXiv: alg-geom/9607012 ]
  56. A. Braverman, “On quantum flag algebras”, [ PDF: English, arXiv: hep-th/9411126 ]
  57. A. Braverman, D. Gaitsgory, “The Poincare-Birkhoff-Witt theorem for quadratic algebras of Koszul type”, Journal of Algebra 181 (2), 315-328 [ PDF: English, arXiv: hep-th/9411113 ]