Representation theory, integrable systems, algebraic geometry, mathematical aspects of string theory and quantum field theory.
Teaching [List of my courses]
In Summer 2020 I teach MATH 53 Multivariable Calculus
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
Toroidal q-Opers [2007.11786] Submitted to Annales Henri Poincare
q-Opers, QQ-Systems, and Bethe Ansatz [2002.07344] Submitted to JEMS
(SL(N),q) -opers, the q-Langlands correspondence, and quantum/classical duality [1811.09937] Submitted to Comm.Math.Phys.
A-type Quiver Varieties and ADHM Moduli Spaces [1805.00986] Submitted to Comm.Math.Phys.
qKZ/tRS Duality via Quantum K-Theoretic Counts [1802.04463] Accepted in Math. Res. Lett.
Quantum K-theory of Quiver Varieties and Many-Body Systems [1705.10419] Submitted to Selecta Math.
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
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]
Other Teaching Activities
I teach math to school kids at the Berkeley 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 teach 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.