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] 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

 

更新时间: 2025-05-07 17:04:14