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      Moebius Foundation Fellowship      Moscow, Russia
  • 2008      Weisskopf Diploma      Erice, Italy
  • 2007      Dynasty Foundation Fellowship      Moscow, Russia

Publication

  • [1] 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, 20, 077 (2024)
  • [2] S. Arthamonov, Sh. Shakirov, An Elliptic Generalization of A1 Spherical DAHA at K=2, IMRN, 19, 13046–13084 (2024)
  • [3] Sh. Shakirov, Non-stationary difference equation for q-Virasoro conformal blocks, Lett. Math. Phys., 114(115) (2024)
  • [4] 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)
  • [5] A. Gorsky, P. Koroteev, O. Koroteeva, Sh. Shakirov, Double Inozemtsev limits of the quantum DELL system, Physics Letters B, 826, 136919 (2022)
  • [6] C. Kozcaz, Sh. Shakirov and W. Yan, Argyres-Douglas Theories, Modularity of Minimal Models and Refined Chern-Simons, Adv. Theor. Math. Phys., 26(3), 643-672 (2022)
  • [7] Sh. Shakirov and A. Sleptsov, Quantum Racah matrices and 3-strand braids in representation [3,3], J. Geom. Phys., 166, 104273 (2021)
  • [8] C. Kozcaz, Sh. Shakirov, C. Vafa and W. Yan, Refined Topological Branes, Comm. Math. Phys., 385, 937–961 (2021)
  • [9] A.Morozov, A.Popolitov and Sh. Shakirov, Harer-Zagier formulas for knot matrix models, Phys. Lett. B, 818, 136370 (2021)
  • [10] P.Koroteev and Sh.Shakirov, The quantum DELL system, Letters in Mathematical Physics, 110(5), 969-999 (2020)
  • [11] R. Lodin, A. Popolitov, Sh. Shakirov and M. Zabzine, Solving q-Virasoro constraints, Lett. Math. Phys., 110, 179–210 (2020)
  • [12] A.Morozov, A.Popolitov and Sh. Shakirov, Quantization of Harer-Zagier formulas, Phys. Lett. B, 811, 135932 (2020)
  • [13] S.Arthamonov and Sh.Shakirov, Refined Chern-Simons Theory in Genus Two, J. Knot Theory Ram., 29(07), 2050044 (2020)
  • [14] S.Arthamonov and Sh.Shakirov, Genus Two Generalization of A1 spherical DAHA, Selecta Mathematica, 25, 17 (2019)
  • [15] A. Morozov, A. Popolitov and Sh. Shakirov, On (q,t)-deformation of Gaussian matrix model, Phys. Lett. B, 784, 342-344 (2018)
  • [16] 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)
  • [17] C. Cordova, B. Heidenreich, A. Popolitov, Sh. Shakirov, Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models, Comm. Math. Phys., 361, 1235–1274 (2018)
  • [18] M. Aganagic and Sh. Shakirov, Gauge/Vortex duality and AGT, New Dualities of Supersymmetric Gauge Theories, 419-448 (2015)

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: 2025-05-20 15:34:25