Teaching Statement
Papers published in journals:
32. Y. Kononov, A. Smirnov, Pursuing quantum difference equations I: stable envelopes of subvarieties, Lett. Math. Phys., 112:69, (2022)
31. Y. Kononov, A. Smirnov, Pursuing quantum difference equations II: 3D-mirror symmetry, Int. Res. Math. Not. (2022),
30. A. Okounkov, A. Smirnov, Quantum difference equation for Nakajima varieties,
Inventiones mathematicae, 131, (2022)
29. H. Dinkins, A.Smirnov, Euler characteristic of stable envelopes,
Selecta Mathematica, (2022)
28. H. Dinkins, A. Smirnov, Capped vertex with descendants for zero dimensional A_{∞} quiver varieties, Adv. in Math., 401, (2022)
27. A. Smirnov, Z. Zhou, 3d Mirror Symmetry and Quantum K-theory of Hypertoric Varieties, Adv. in Math., 395, (2022)
26. H. Dinkins, A.Smirnov, Quasimaps to zero-dimensional A_{∞}-quiver varieties, Int. Math. Res. Not., 2, 1123–1153,(2020)
25. H. Dinkins, A. Smirnov, Characters of tangent spaces at torus fixed points and 3d-mirror symmetry, Lett. Math. Phys., 110, 2337–2352, (2020)
24. R. Rimányi, A. Smirnov, A. Varchenko, Z. Zhou, Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety, SIGMA, 15 (2019)
23. R. Rimányi, A. Smirnov, A. Varchenko, Z. Zhou , 3d Mirror Symmetry and Elliptic Stable Envelopes, Int. Math. Res. Not., 13, 10016–10094, (2022)
22. P. Koroteev, P. Pushkar, A. Smirnov, A. Zeitlin, Quantum K-theory of Quiver Varieties and Many-Body Systems, Selecta Mathematica, 27: 81, (2021)
21. P. Pushkar, A. Smirnov, A. Zeitlin, Baxter Q-operator from quantum K-theory, Adv. in Math., 360, (2020)
20. A. Smirnov, Elliptic stable envelope for Hilbert scheme of points in the plane, Selecta Mathematica, 26: 3, (2020)
19. A. Smirnov, On the Instanton R-matrix, Commun. in Math. Phys., 345, 703-740, (2016)
18. G. Aminov, S. Arthamonov, A. Smirnov, A. Zotov, Rational Top and its Classical R-matrix, J. of Phys. A: Math. and Theor., 47,1-19, (2014)
17. A. Morozov, A. Smirnov, Towards the proof of AGT relations with the help of the generalized Jack polynomials, Lett. Math. Phys., 104, 585-612, (2014)
16. A. Mironov, A. Morozov, A. Sleptsov, A. Smirnov, On genus expansion of superpolynomials, Nucl. Phys. B, 889, 757-777, (2014)
15. A. Zotov, A. Smirnov, Modifications of bundles, elliptic integrable systems, and related topics, Theor. and Math. Phys., 177, 1281 – 1338, (2013)
14. P. Dunin-Barkowski, A. Mironov, A. Morozov, A. Sleptsov, A. Smirnov, Superpolynomials for toric knots from evolution induced by cut-and-join operators, JHEP 03, 021, 1-85, (2013)
13. A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices, J. of Phys. A: Math. and Theor., 46, 1-25, (2013)
12. A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles, SIGMA, 8 095, 1-37, (2012)
11. D. Galakhov, A. Mironov, A. Morozov, A. Smirnov, On 3d extensions of AGT relation, Theor. and Math. Phys., 172, 939-962, (2012)
10. A. Mironov, A. Morozov, Sh. Shakirov, A. Smirnov, Proving AGT conjecture as HS duality: extension to five dimensions, Nucl. Phys. B, 855, 128-151, (2011)
9. P. Dunin-Barkowski, A. Sleptsov, A. Smirnov, Explicit computation of Drinfeld associator in the case of the fundamental representation of gl_n, J. of Phy. A: Math. and Theor., 45, 1-15, (2012)
8. P. Dunin-Barkowski, A. Sleptsov, A. Smirnov, Kontsevich integral for knots and Vassiliev invariants, Int. J. of Mod. Phys. A, 28, 1-38, (2013)
7. A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, Characteristic Classes and Integrable Systems for Simple Lie Groups, J. of Geom. and Phys., 62, 1810–1850, (2010)
6. A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, Characteristic Classes and Hitchin Systems. General Construction, Commun. in Math. Phys., 316, 1–44, (2012)
5. A. Morozov, A. Smirnov, Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix, Nuclear Physics B, 835, 284-313, (2010)
4. A. Smirnov, Notes on Chern-Simons Theory in the Temporal Gauge, Proceedings of 47th International School of Subnuclear Physics, Erice, Italy, pages 489-499, (2009) https://doi.org/10.1142/9789814374125_0018 , arXiv:0910.5011
3. A. Smirnov, Degenerate Sklyanin Algebras, Cent. Eur. J. of Phys., 8, 542-554, (2009)
2. A. Smirnov, Correspondence between Calogero-Moser systems and integrable SL(N) Euler-Arnold tops, Theor. and Math. Phys., 158, 300-312, (2008)
1. A. Smirnov, Two body systems from sl(2,C)-tops, Theor. and Math. Phys., 157, 8-21, (2007)
Preprints:
3. A. Smirnov, Quantum differential and difference equations for Hilb^n(C^2),
77 pages, (2020) submitted for publication, arXiv:2102.10726
2. A. Smirnov, Rationality of capped descendent vertex in K-theory,
31 pages, arXiv:1612.01048
1. A. Smirnov, Polynomials associated with fixed points on the instanton moduli space, 22 pages, arXiv:1404.5304