BIMSA > 沙米尔·沙基洛夫
助理研究员 沙米尔·沙基洛夫

团队: 数学物理

办公室: A15-302

邮箱: shakirov@bimsa.cn

研究方向: 数学物理

个人主页: https://www.bimsa.net/people/ShamilShakirov/

CV

个人简介

我是一名数学家，研究表示论，重点研究几何关系，尤其是拓扑学（结、链和 3 流形的量子群不变量、曲面的映射类群、q-skein 和双仿射赫克代数）和代数几何（与上同调和 Nakajima 箭筒簇的 K 理论相关的量子 Virasoro 和 W 代数的表示）。数学物理（拓扑量子场论、可积系统、瞬子和弦数学相互作用）在这些领域的作用和重要性已得到越来越多的认可；我的研究很大程度上受到数学物理进展的启发，并受益于与物理学家的长期合作。这幅图景与我对概率接口的研究（可积概率系统、麦克唐纳过程和随机矩阵）以及对经典不变量理论（曲线和曲面的不变量、张量、判别式和代数方程的结式）的长期兴趣相得益彰。我最近的研究项目的主要成果包括：构造双仿射赫克代数的二类比 [14]、建立双椭圆广义麦克唐纳差分方程 [8]、开发一种计算麦克唐纳过程可观测量的新方法 [22]、证明平面曲线凯莱不变量的行列式公式 [24] 等。

研究兴趣

  • 表示论
  • 拓扑
  • 数学物理

教育经历

  • 2011 - 2015      University of California Berkeley      Mathematics      Ph.D      (Supervisor: Prof. Aganagic, Prof. Reshetikhin)
  • 2005 - 2009      Moscow Institute of Physics and Technology      Physics and Mathematics      M.Sc.      (Supervisor: Prof. Morozov)
  • 2002 - 2005      Kazan State University      Physics      Diploma      (Supervisor: Prof. Aminova)

工作经历

  • 2024 -      Beijing Institute of Mathematical Sciences and Applications      Assistant Professor      tenure track
  • 2023 - 2024      Institute for Information Transmission Problems      Senior Researcher
  • 2021 - 2022      University of Geneve Switzerland      Senior Researcher
  • 2019 - 2019      Uppsala University      Researcher
  • 2015 - 2018      Harvard University      Junior Fellow

荣誉与奖项

出版物

  • [1] S. Arthamonov, Sh. Shakirov, An Elliptic Generalization of A1 Spherical DAHA at K = 2, International Mathematics Research Notices, 2024(19), 13046-13084 (2024)
  • [2] Sh. Shakirov, Non-stationary difference equation for-Virasoro conformal blocks, Letters in Mathematical Physics, 114(5), 115 (2024)
  • [3] H.Awata, K.Hasegawa, H.Kanno, R.Ohkawa, Sh.Shakirov, J.Shiraishi, Y.Yamada, Non-stationary difference equation and affine Laumon space II: Quantum Knizhnik-Zamolodchikov equation, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 20, 077 (2024)
  • [4] A Mironov, A Morozov, A Popolitov, S Shakirov, Deformation of superintegrability in the Miwa-deformed Gaussian matrix model, Physical Review D, 110(4), 046027 (2024)
  • [5] A Mironov, A Morozov, A Popolitov, S Shakirov, Summing up perturbation series around superintegrable point, Physics Letters B, 852, 138593 (2024)
  • [6] S. Arthamonov, Sh. Shakirov, An Elliptic Generalization of A1 Spherical DAHA at K=2, IMRN, 19, 13046–13084 (2024)
  • [7] H Awata, K Hasegawa, H Kanno, R Ohkawa, S Shakirov, J Shiraishi et al., Non-stationary difference equation and affine Laumon space: quantization of discrete Painlevé equation, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 19, 089 (2023)
  • [8] H.Awata, K.Hasegawa, H.Kanno, R.Ohkawa, Sh.Shakirov, J.Shiraishi, Y.Yamada, Non-stationary difference equation and affine Laumon space: Quantization of discrete Painlev’e equation, SIGMA, 19, 089 (2023)
  • [9] A. Gorsky, P. Koroteev, O. Koroteeva, Sh. Shakirov, Double Inozemtsev limits of the quantum DELL system, Physics Letters B, 826, 136919 (2022)
  • [10] S Shakirov, A Sleptsov, Quantum Racah matrices and 3-strand braids in representation [3, 3], Journal of Geometry and Physics, 166, 104273 (2021)
  • [11] A.Morozov, A.Popolitov and Sh. Shakirov, Harer-Zagier formulas for knot matrix models, Physics Letters B, 818, 136370 (2021)
  • [12] C. Kozcaz, Sh. Shakirov, C. Vafa and W. Yan, Refined topological branes, Communications in Mathematical Physics, 385, 937-961 (2021)
  • [13] Sh. Shakirov and A. Sleptsov, Quantum Racah matrices and 3-strand braids in representation [3,3], J. Geom. Phys., 166, 104273 (2021)
  • [14] A.Morozov, A.Popolitov and Sh. Shakirov, Quantization of Harer-Zagier formulas, Physics Letters B, 811, 135932 (2020)
  • [15] S Arthamonov, S Shakirov, Refined Chern–Simons theory in genus two, Journal of Knot Theory and Its Ramifications, 29(7), 2050044 (2020)
  • [16] P.Koroteev and Sh.Shakirov, The quantum DELL system, Letters in Mathematical Physics, 110(5), 969-999 (2020)
  • [17] R. Lodin, A. Popolitov, Sh. Shakirov and M. Zabzine, Solving q-Virasoro constraints, Letters in Mathematical Physics, 110(1), 179-210 (2020)
  • [18] S.Arthamonov and Sh.Shakirov, Refined Chern-Simons Theory in Genus Two, J. Knot Theory Ram., 29(07), 2050044 (2020)
  • [19] S Arthamonov, S Shakirov, Genus two generalization of$ A 1 $spherical DAHA, Selecta Mathematica, 25, 1-29 (2019)
  • [20] S.Arthamonov and Sh.Shakirov, Genus Two Generalization of A1 spherical DAHA, Selecta Mathematica, 25, 17 (2019)
  • [21] A Morozov, A Popolitov, S Shakirov, On (q, t)-deformation of Gaussian matrix model, Physics Letters B, 784, 342-344 (2018)
  • [22] C. Cordova, B. Heidenreich, A. Popolitov, Sh. Shakirov, Orbifolds and exact solutions of strongly-coupled matrix models, Communications in Mathematical Physics, 361, 1235-1274 (2018)
  • [23] L Bishler, A Morozov, S Shakirov, A Sleptsov, On the block structure of the quantum$ℛ$-matrix in the three-strand braids, International Journal of Modern Physics A, 33(17), 1850105 (2018)
  • [24] C. Kozcaz, Sh. Shakirov and W. Yan, Argyres-Douglas theories, modularity of minimal models and refined Chern-Simons, arXiv preprint arXiv:1801.08316, 26, 643-672 (2018)
  • [25] L. Bishler, An. Morozov, A. Sleptsov and Sh. Shakirov, On the block structure of the quantum R-matrix in the three-strand braids, Int. J. Mod. Phys. A, 33(17), 1850105 (2018)
  • [26] A. Morozov, A. Popolitov and Sh. Shakirov, On (q,t)-deformation of Gaussian matrix model, Phys. Lett. B, 784, 342-344 (2018)
  • [27] A Borodin, I Corwin, V Gorin, S Shakirov, Observables of Macdonald processes, Transactions of the American Mathematical Society, 368(3), 1517-1558 (2016)
  • [28] M. Aganagic and Sh. Shakirov, Gauge/Vortex duality and AGT, , 419-448 (2015)
  • [29] A Popolitov, S Shakirov, On undulation invariants of plane curves, Michigan Mathematical Journal, 64(1), 143-153 (2015)
  • [30] M Aganagic, S Shakirov, Knot homology and refined Chern–Simons index, Communications in Mathematical Physics, 333, 187-228 (2015)
  • [31] S Shakirov, Applications of Macdonald ensembles, University of California, Berkeley (2015)
  • [32] M Aganagic, N Haouzi, S Shakirov, $A_n$-Triality, arXiv preprint arXiv:1403.3657 (2014)
  • [33] S Shakirov, Colored knot amplitudes and Hall-Littlewood polynomials, arXiv preprint arXiv:1308.3838 (2013)
  • [34] M Aganagic, S Shakirov, Refined Chern-Simons theory and topological string, arXiv preprint arXiv:1210.2733 (2012)
  • [35] A Mironov, A Morozov, S Shakirov, Torus HOMFLYPT as the Hall–Littlewood polynomials, Journal of Physics A: Mathematical and Theoretical, 45(35), 355202 (2012)
  • [36] A Mironov, A Morozov, S Shakirov, A Sleptsov, Interplay between MacDonald and Hall-Littlewood expansions of extended torus superpolynomials, Journal of High Energy Physics, 2012(5), 1-12 (2012)
  • [37] AD Mironov, AY Morozov, AV Popolitov, SR Shakirov, Resolvents and Seiberg-Witten representation for a Gaussian-ensemble, Theoretical and Mathematical Physics, 171, 505-522 (2012)
  • [38] A Morozov, S Shakirov, Resultants and contour integrals, Functional Analysis and Its Applications, 46(1), 33-40 (2012)
  • [39] A Mironov, A Morozov, S Shakirov, A Smirnov, Proving AGT conjecture as HS duality: extension to five dimensions, Nuclear Physics B, 855(1), 128-151 (2012)
  • [40] A Mironov, A Morozov, S Shakirov, Towards a proof of AGT conjecture by methods of matrix models, International Journal of Modern Physics A, 27 (2012)
  • [41] M Aganagic, S Shakirov, Refined Chern-Simons theory and knot homology, Proc. Symp. Pure Math, 85, 3-32 (2012)
  • [42] S Shakirov, Beta deformation and superpolynomials of (n, m) torus knots, arXiv preprint arXiv:1111.7035 (2011)
  • [43] M Aganagic, S Shakirov, Knot homology from refined Chern-Simons theory, arXiv preprint arXiv:1105.5117 (2011)
  • [44] A Mironov, A Morozov, S Shakirov, Brezin-Gross-Witten model as “pure gauge” limit of Selberg integrals, Journal of High Energy Physics, 2011(3), 1-25 (2011)
  • [45] A Morozov, S Shakirov, Analogue of the identity Log Det= Trace Log for resultants, Journal of Geometry and Physics, 61(3), 708-726 (2011)
  • [46] S Shakirov, Exact solution for mean energy of 2d Dyson gas at β= 1, Physics Letters A, 375(6), 984-989 (2011)
  • [47] A Mironov, A Morozov, S Shakirov, A direct proof of AGT conjecture at β= 1, Journal of High Energy Physics, 2011(2), 1-41 (2011)
  • [48] A Mironov, A Morozov, S Shakirov, On the ‘Dotsenko–Fateev’representation of the toric conformal blocks, Journal of Physics A: Mathematical and Theoretical, 44(8), 085401 (2011)
  • [49] A Morozov, S Shakirov, The matrix model version of AGT conjecture and CIV-DV prepotential, Journal of High Energy Physics, 2010(8), 1-37 (2010)
  • [50] A Morozov, S Shakirov, From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators, arXiv preprint arXiv:1007.4100 (2010)
  • [51] A Mironov, A Morozov, S Shakirov, Conformal blocks as Dotsenko–Fateev integral discriminants, International Journal of Modern Physics A, 25(16), 3173-3207 (2010)
  • [52] SR Shakirov, Nonperturbative approach to finite-dimensional non-Gaussian integrals, Theoretical and Mathematical Physics, 163(3), 804-812 (2010)
  • [53] AY Morozov, SR Shakirov, New and old results in resultant theory, Theoretical and Mathematical Physics, 163, 587-617 (2010)
  • [54] A Mironov, A Morozov, S Shakirov, Matrix model conjecture for exact BS periods and Nekrasov functions, Journal of High Energy Physics, 2010(2), 1-26 (2010)
  • [55] A Morozov, S Shakirov, Introduction to integral discriminants, Journal of High Energy Physics, 2009(12), 002 (2009)
  • [56] A Morozov, S Shakirov, Exact 2-point function in Hermitian matrix model, Journal of High Energy Physics, 2009(12), 003 (2009)
  • [57] ET Akhmedov, S Shakirov, Gluings of surfaces with polygonal boundaries, Functional Analysis and Its Applications, 43(4), 245-253 (2009)
  • [58] N Perminov, S Shakirov, Discriminants of symmetric polynomials, arXiv preprint arXiv:0910.5757 (2009)
  • [59] A Morozov, S Shakirov, On equivalence of two Hurwitz matrix models, Modern Physics Letters A, 24(33), 2659-2666 (2009)
  • [60] AS Anokhina, AY Morozov, SR Shakirov, Resultant as the determinant of a Koszul complex, Theoretical and Mathematical Physics, 160, 1203-1228 (2009)
  • [61] A Morozov, S Shakirov, Generation of matrix models by Ŵ-operators, Journal of High Energy Physics, 2009(04), 064 (2009)
  • [62] VV Dolotin, AY Morozov, SR Shakirov, Anstructure on simplicial complexes, Theoretical and Mathematical Physics, 156, 965-995 (2008)
  • [63] V Dolotin, A Morozov, S Shakirov, Higher nilpotent analogues of A∞-structure, Physics Letters B, 651(1), 71-73 (2007)
  • [64] S Shakirov, Higher discriminants of polynomials, arXiv preprint math/0609524 (2006)

Selected Publications:

Knot Homology from Refined Chern-Simons Theory (with M. Aganagic), 
Comm.Math.Phys. 333 (2015) 187-228
https://doi.org/10.1007/s00220-014-2197-4
http://arxiv.org/abs/1105.5117

Observables of Macdonald processes (with A. Borodin, I. Corwin, V. Gorin), 
Trans. Amer. Math. Soc. 368 (2016) 1517-1558
https://doi.org/10.1090/tran/6359
http://arxiv.org/abs/1306.0659

Genus Two Generalization of A1 spherical DAHA (with S.Arthamonov), 
Selecta Mathematica 25 (2019) 17
https://doi.org/10.1007/s00029-019-0447-1
http://arxiv.org/abs/1704.02947

An Elliptic Generalization of A1 Spherical DAHA at K=2 (with S.Arthamonov), 
International Mathematics Research Notices 19 (2024) 13046–13084
https://doi.org/10.1093/imrn/rnae192
https://arxiv.org/abs/2306.00215

Non-stationary difference equation for q-Virasoro conformal blocks, 
Letters in Mathematical Physics 114 (2024) 115
https://doi.org/10.1007/s11005-024-01856-2
https://arxiv.org/abs/2111.07939

 

更新时间: 2025-07-27 15:00:07