BIMSA > Shamil Shakirov
Assistant Professor Shamil Shakirov

Group: Mathematical Physics

Office: A15-302

Email: shakirov@bimsa.cn

Research Field: Mathematical Physics

Webpage: https://www.bimsa.net/people/ShamilShakirov/

CV

Biography

I am a mathematician working in the field of Representation Theory with focus on relation to geometry, particularly Topology (quantum group invariants of knots, links and 3-manifolds, mapping class groups of surfaces, q-skein and double affine Hecke algebras) and Algebraic Geometry (representations of quantum Virasoro and W-algebras associated with cohomology and K-theory of Nakajima quiver varieties). The role and importance of Mathematical Physics (topological quantum field theory, integrable systems, instantons and the String-Math interaction) in these domains has been increasingly recognized; my research is substantially inspired by advances in mathematical physics and benefits from recurring collaboration with physicists. This picture is complemented by my work on the interface with Probability (integrable probabilistic systems, Macdonald processes and random matrices) and a long-standing interest in Classical Invariant Theory (invariants of curves and surfaces, tensors, discriminants and resultants of algebraic equations). Key recent results that illustrate my research program include construction of a genus two analogue of the double affine Hecke algebra [14], formulation of a double elliptic generalization of Macdonald difference equations [8], development of a new method to compute observables of Macdonald processes [22], proof of a determinantal formula for the Cayley invariant of plane curves [24] among others.

Research Interest

  • Representation Theory
  • Topology
  • Mathematical Physics

Education Experience

  • 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)

Work Experience

  • 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

Honors and Awards

  • 2017      Milton Fund Award      Cambridge, USA
  • 2015      Harvard Junior Fellowship      Cambridge, USA
  • 2008      Weisskopf Diploma      Erice, Italy
  • 2008      Moebius Foundation Fellowship      Moscow, Russia
  • 2007      Dynasty Foundation Fellowship      Moscow, Russia

Publication

  • [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

 

Update Time: 2025-08-12 17:00:08