Representation theory, algebraic geoemtry, integrable systems, mathematical aspects of string theory and quantum field theory.
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
Workshops on Elliptic Integrable Systems: 2022 Edition, 2021 EditionIn 2020 I was awarded AMS-Simons grant
Teaching [List of my courses]
Selected Publications [Complete list]
[Arxiv] [MathSciNet] [Inspire HEP] [RG] [Google Scholar]
Algebraic Geometry and Representation Theory
Branes and DAHA Representations. (with A. Gukov, S. Nawata, D. Pei, I. Saberi) [2206.03565] SpringerBriefs ISBN 978-3-031-28154-9 (2023) Monograph
3d Mirror Symmetry for Instanton Moduli Spaces. (with A. Zeitlin) [2105.00588] Commun. Math. Phys. 403, 1005–1068 (2023)
Toroidal q-Opers (with A. Zeitlin) [2007.11786] J. of the Inst. of Math. of Jussieu, (2021) 1-62
q-Opers, QQ-Systems, and Bethe Ansatz II: Generalized Minors (with A. Zeitlin) [2108.04184] J. Reine Angew. Math. (Crelle J.) (2023) 271
q-Opers, QQ-Systems, and Bethe Ansatz. (with E. Frenkel, D. Sage, A. Zeitlin) [2002.07344] J. Eur. Math. Soc. (2023)
(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] Selecta 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)
Recent and Upcoming Conferences and Seminars
See [Complete list] for slides, notes and videos
Algebra Seminar, University of Buffalo, NY [link][notes]
Workshop Elliptic Integrable Systems, Representation Theory, and Hypergeometric Functions, Tokyo, Japan [link][slides]
Workshop Dualities and Symmetries in Integrable Systems, Sabhal Mor Ostaig, Isle of Skye, Scotland, UK [link][slides]
Workshop Gauge Linear Sigman Models @30, Simons Center for Geometry and Physics, Stony Brook, NY [link][slides]
Workshop 50 Years of Supersymmetry, University of Minnesota, MN [link][slides]
Special Colloquium at University of Sheffield, Sheffield, England [slides]
Special Colloquium at Heriot-Watt University, Edinburgh, Scotland [slides]
Special Colloquium at Ohio State University, Columbus, OH [link][slides]
Special Colloquium at University of Montreal, Quebec, Canada [slides]
Simons Center Program on Geometric and Representation-Theoretic Aspects of Quantum Integrability [slides][video]
All Australia Math Physics Colloquium (over Zoom)[slides]
Math Physics Seminar, University of Queensland, Australia [slides]
Mathematics Colloquium, Australian National University, Canberra, Australia [slides]
Math Physics Seminar, University of Melbourne, Australia [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 0 712.1136 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. Slides of my talk on Fractals
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.