Representation theory, integrable systems, algebraic geometry, mathematical aspects of string theory and quantum field theory.
Zoom workshop Elliptic Integrable Systems (March 7-9th 2021)
SCGP Program Geometric and Representation-Theoretic Aspects of Quantum Integrability (August 29th - October 21st 2022) with focus workshop Geometric Representation Theory, Integrability, and Supersymmetric Gauge Theories
Teaching [List of my courses]
Selected Publications [Complete list]
[Arxiv] [MathSciNet] [Inspire HEP] [RG]
Below I list selected publications on several topics in math and physics
Algebraic Geometry and Representation Theory
3d Mirror Symmetry for Instanton Moduli Spaces. (with A. Zeitlin) [2105.00588]
Toroidal q-Opers (with A. Zeitlin) [2007.11786] Accepted to J. Inst. Math. Jussieu
q-Opers, QQ-Systems, and Bethe Ansatz. (with E. Frenkel, D. Sage, A. Zeitlin) [2002.07344] Accepted in J. Europ. Math. Soc.
(SL(N),q)-opers, the q-Langlands correspondence, and quantum/classical duality. (with D. Sage, A. Zeitlin) [1811.09937] Commun. Math. Phys. 381, 641–672 (2021)
A-type Quiver Varieties and ADHM Moduli Spaces [1805.00986] Commun. Math. Phys. 381, 175–207 (2021)
qKZ/tRS Duality via Quantum K-Theoretic Counts. (with A. Zeitlin) [1802.04463] Math. Res. Lett. 28, no. 2, 435–470 (2021)
Quantum K-theory of Quiver Varieties and Many-Body Systems. (with P. Pushkar, A. Smirnov, A. Zeitlin) [1705.10419] Sel. Math. New Ser. 27, 87 (2021)
Integrable Systems and Supersymmetry
The Quantum DELL System [1906.10354] Lett. Math. Phys. 110, 969–999 (2020)
On Elliptic Algebras and Large-n Supersymmetric Gauge Theories [1601.08238] J. Math. Phys. 57, no. 11, 112302 (2016)
On Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories [1510.00972 ] Lett. Math. Phys. 108, no. 1, 45 (2018)
Defects and Quantum Seiberg-Witten Geometry [1412.6081] JHEP 1505, 095 (2015)
On Three Dimensional Quiver Gauge Theories and Integrability [1304.0779] JHEP 1305, 126 (2013)
BPS States in Omega Background and Integrability [1207.0460] JHEP 1210, 116 (2012)
Quantum Deformations of the One-Dimensional Hubbard Model [0802.0777] J. Phys. A 41, 255204 (2008)
Three-Dimensional Mirror Symmetry
Good IR Duals of Bad Quiver Theories [1712.06068] JHEP 1805, 114 (2018)
On Three-Dimensional Quiver Gauge Theories of Type B [1612.00810] JHEP 1709, 067 (2017)
Mirror Symmetry in Three Dimensions via Gauged Linear Quivers [1402.0016] JHEP 1406, 059 (2014)
Resurgence and Holomorphy: From Weak to Strong Coupling [1410.0388] J. Math.Phys. 56, no. 5, 053505 (2015)
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces [1303.6386] J. Exp. Theor. Phys. 117, 517 (2013)
Nonperturbative Dynamics of QFTs
Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions [1605.01472] Phys. Lett. B 759, 154 (2016)
Quantum Dynamics of Low-Energy Theory on Semilocal Non-Abelian Strings [1107.377 9] Phys. Rev. D 84, 065018 (2011)
Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model [1009.6207] Phys. Rev. D 82, 125023 (2010)
On the Null Energy Condition and Causality in Lifshitz Holography [1007.1428] Phys. Rev. D 82, 084002 (2010)
Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance [0901.4347] Phys. Rev. D 79, 045023 (2009)
On Existence of Self-Tuning Solutions in Static Braneworlds without Singularities [0712.1136] JHEP 0802, 104 (2008)
Recent and Upcoming Conferences and Seminars
See [Complete list] for slides, notes and videos
Mathematics Seminar, Institute for Advanced Study in Mathematics, Zhejiang University, China (over zoom) [notes][video]
Mathematical Physics seminar, Perimeter Institute for Theoretical Physics, Waterloo, ON (over zoom) [notes][video]
Nordita String Seminar, Stockholm, Sweden (over zoom) [notes]
Joint Mathematics Meeting, Denver, CO [slides]
Algebra and Geometry Seminar, California Institute of Technology, Pasadena, CA
Algebra seminar, Virginia Polytechnic, Blacksburg, VA [slides]
AMS Fall 2019 Sectional Meeting, University of California, Riverside [slides]
Geometric Representation Theory and Quantum Field Theories, Tsinghua Sanya International Mathematics Forum, Sanya, China
Representation Theory and Mathematical Physics seminar, UC Berkeley [slides]
Geometry, Physics, and Representation Theory Seminar, Northeastern University, Boston, MA [link] [slides]
Quantum Field Theory seminar, CMSA, Harvard, Cambrdige, MA [link] [slides][video]
Program on Holomorphic Differentials in Mathematics and Physics, MSRI, Berkeley, CA [link]
Program on Quiver varieties and representation theory, Centre de Recherches Mathematiques, Montreal, QC, Canada [link]
Workshop `BPS/CFT Correspondence', Centre International de Rencontres Mathematiques, Marseille, France [link][notes]
Conference on Verlinde Algebra and Grassmannian, Sun Yatsen University, Guangzhou, China [link][slides]
Conference on Higher Symmetries, Aspnen, CO [link][slides]
Geometry seminar, Korean Institute for Advanced Study, Seoul, Korea [slides]
Duluth Winter School 2014 on Supersymmetry and String Theory
University of California, Davis, Department of Mathematics (2016-2018)
Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada (2012-2016)
PhD: University of Minnesota (2012) [My PhD Thesis]
During my Minnesota years I mostly worked on physics of gauge theories with extended supersymmetry in various dimensions.
I was a Graduate Fellow at Kavli Institute for Theoretical Physics in Spring 2012.
MS: Moscow Institute of Physics and Technology (2008) [Paper 0901.4347 is based on my master thesis]
BS: Moscow Institute of Physics and Technology (2006) [Paper 0712.1136 is based on my bachelor diploma]
At Phystech I did undergraduate research at the Institute for Theoretical and Experimental Physics as well as at the Institute for Nuclear Research.
The former together with the Independent University of Moscow taught me math, at the latter I learned some physics.
Other Teaching Activities
I teach math to school kids at the Berkeley Math Circle and at Stanford Math Circle
I serve as a mentor at Hermiona Education which helps grade school students with choosing their higher eduation in the US
In Summer 2019 I tought at Sichuan Univeristy, Chengdu, China as a part of Lion education program. Slides of my public lecture on black holes and entanglement.
I enjoy doing endurance sports: biking, running (my last marathon), cross country skiing.
My Strava profile
My wife is also a scientist, at the moment she is a graduate student at Physics Department of University of Minnesota. Together we have daughter Anna.