Research Interests

My research interests are in Representation Theory (particularly, in Cherednik algebras, quantum affine and toroidal algebras, shuffle algebras, shifted quantum affine algebras and Yangians) and its connection to Algebraic Geometry (via Laumon spaces, Nakajima quiver varieties, Coulomb branches) and Integrable Systems (the Toda-like integrable systems and the quantum inverse scattering method)

My research has been supported by NSF Grants No. DMS-1502497 (changed to DMS-1821185) and DMS-2001247 (changed to DMS-2037602)

CV: here


Assistant Professor, Purdue University, 2020‒present
Gibbs Assistant Professor, Yale University, 2017‒2020
Research Assistant Professor, Simons Center for Geometry and Physics, 2014‒2017


PhD, Mathematics, Massachusetts Institute of Technology, 2014
MS, Mathematics, Moscow State University, 2009
MS, Mathematics, Independent University of Moscow, 2009

Publications (arXiv)

  • Rational Lax matrices from antidominantly shifted extended Yangians: BCD types (with R. Frassek)
    Submitted; Preprint arXiv:2104.14518 (65pp, last update on 07/12/2021) (arXiv)
  • Surface defects in gauge theory and KZ equation (with N. Nekrasov)
    Submitted; Preprint arXiv:2103.12611 (41pp, last update on 07/13/2021) (arXiv)
  • Quantum loop groups and shuffle algebras via Lyndon words (with A. Negut)
    Submitted; Preprint arXiv:2102.11269 (75pp, last update on 02/22/2021) (arXiv)
  • Lax matrices from antidominantly shifted Yangians and quantum affine algebras (with R. Frassek and V. Pestun)
    Submitted; Preprint arXiv:2001.04929 (54pp, last update on 01/14/2020) (arXiv)
  • Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data
    Letters in Mathematical Physics 110 (2020), no. 8, 2083-2111 (journal) (arXiv)
  • Duality of Lusztig and RTT integral forms of $U_v(L\mathfrak{sl}_n)$
    Journal of Pure and Applied Algebra 225 (2021), DOI:10.1016/j.jpaa.2020.106469, 14pp (journal) (arXiv)
  • Shifted quantum affine algebras: integral forms in type A (with M. Finkelberg; appendices joint with A. Weekes)
    Arnold Mathematical Journal 5 (2019), no. 2, 197‒283 (journal) (arXiv)
  • PBWD bases and shuffle algebra realizations for $U_v(L\mathfrak{sl}_n), U_{v_1,v_2}(L\mathfrak{sl}_n), U_v(L\mathfrak{sl}(m|n))$ and their integral forms
    Selecta Mathematica (New Series) 27 (2021), DOI:10.1007/s00029-021-00634-5, 48pp (journal) (arXiv)
  • On Sevostyanov's construction of quantum difference Toda lattices (with R. Gonin)
    International Mathematics Research Notices (2019), DOI:10.1093/imrn/rnz083, 61pp (journal) (arXiv)
  • Multiplicative slices, relativistic Toda and shifted quantum affine algebras (with M. Finkelberg)
    Representations and Nilpotent Orbits of Lie Algebraic Systems (special volume in honour of the 75th birthday of Tony Joseph), Progress in Mathematics 330 (2019), 133‒304 (journal) (arXiv)
  • Classical limits of quantum toroidal and affine Yangian algebras
    Journal of Pure and Applied Algebra 221 (2017), no. 10, 2633‒2646 (journal) (arXiv)
  • Several realizations of Fock modules for toroidal $\ddot{U}_{q,d}(\mathfrak{sl}_n)$
    Algebras and Representation Theory 22 (2019), no. 1, 177‒209 (journal) (arXiv)
  • Homomorphisms between different quantum toroidal and affine Yangian algebras (with M. Bershtein)
    Journal of Pure and Applied Algebra 223 (2019), no. 2, 867‒899 (journal) (arXiv)
  • Bethe subalgebras of $U_q(\widehat{\mathfrak{gl}}_n)$ via shuffle algebras (with B. Feigin)
    Selecta Mathematica (New Series) 22 (2016), no. 2, 979‒1011 (journal) (arXiv)
  • The affine Yangian of $\mathfrak{gl}_1$ revisited
    Advances in Mathematics 304 (2017), 583‒645 (journal) (arXiv)
  • Infinitesimal Hecke algebras of $\mathfrak{so}_N$
    Journal of Pure and Applied Algebra 219 (2015), no. 6, 2046‒2061 (journal) (arXiv)
  • Infinitesimal Cherednik algebras as W-algebras (with I. Losev)
    Transformation Groups 19 (2014), no. 2, 495‒526 (journal) (arXiv)
  • Representations of infinitesimal Cherednik algebras (with F. Ding)
    Representation Theory (electronic) 17 (2013), 557‒583 (journal) (arXiv)
  • Equivariant K-theory of Hilbert schemes via shuffle algebra (with B. Feigin)
    Kyoto Journal of Mathematics 51 (2011), no. 4, 831‒854 (journal) (arXiv) (updated)
  • Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces
    Selecta Mathematica (New Series) 16 (2010), no. 2, 173‒200 (journal) (errata) (arXiv) (updated)

Teaching Experience

  • Spring 2021: Lecturer for MA 59800CIDLA (Infinite-dimensional Lie algebras and applications) at Purdue web-page
  • Fall 2020: Lecturer for MA 26500 (Linear Algebra) at Purdue web-page
  • Fall 2019: Lecturer for MATH 120 (Calculus of Functions of Several Variables) at Yale web-page
  • Spring 2019: Lecturer for MATH 754 (Infinite-dimensional Lie algebras and applications) at Yale web-page
  • Fall 2018: Lecturer for MATH 353 (Introduction to Representation Theory) at Yale web-page
  • Fall 2018: Lecturer for MATH 120 (Calculus of Functions of Several Variables) at Yale web-page
  • Spring 2018: Lecturer for MATH 667 (Topics in Quantum Groups and Representation Theory) at Yale web-page
  • Fall 2017: Lecturer for MATH 120 (Calculus of Functions of Several Variables) at Yale web-page
  • Fall 2016: Head instructor for MAT 118 (Mathematical Thinking) at SBU web-page
  • Fall 2015: Lecturer for MAT 126 (Calculus B) at SBU
  • Fall 2014: Section leader for MAT 303 (Calculus IV with Applications) at SBU
  • Spring 2014: Teaching assistant for Math 18.100B (Real Analysis) at MIT web-page
  • Winter 2014: Mentor in the MIT Directed Reading Program (Representation Theory) web-page
  • Fall 2012: Section leader for Math 18.02 (Multivariable Calculus) at MIT web-page
  • 2011‒2013: Grader for MIT courses 18.100B (Real Analysis), 18.125 (Real and Functional Analysis), 18.01 (Calculus), 18.782 (Introduction to Arithmetic Geometry), 18.705 (Commutative Algebra), and 18.737 (Algebraic Groups)

Mentoring at MIT PRIMES program

I had mentored Fengning Ding during 2011‒2013 in the MIT PRIMES program. With our project "Representations of infinitesimal Cherednik algebras", Fengning won the 4th Prize at 2012 Intel STS US national competition (\$40,000 award) and became 2012 Davidson Fellow Laureate (\$50,000 award).

MIT PRIMES is a free, year-long after-school research program for high school students from the Boston area. Program participants work with MIT researchers on exciting unsolved problems in mathematics, computer science, and computational biology.

Notes for Old Selected Talks

  • Temple University, Algebra Seminar, November 2015
    Relation between quantum toroidal algebras of $\mathfrak{sl}_n$ and affine Yangians of $\mathfrak{sl}_{nm}$ (handwritten notes)
  • Yale University, Geometry, Symmetry and Physics Seminar, April 2015
    Shuffle realization of $\ddot{U}_{q,d}(\mathfrak{sl}_n)$ and Bethe subalgebras of $U_q(\widehat{\mathfrak{gl}}_n)$ (handwritten notes)
  • Northeastern University, Graduate student seminar, April 2014
    The affine Yangian and the quantum toroidal of $\mathfrak{gl}_1$ (handwritten notes)
  • MIT-NEU, Graduate seminar on Quantum cohomology and Representation theory, February 2014
    Geometric representation theory of the Hilbert schemes (pdf notes I) (pdf notes II) (pdf notes III)
  • Northeastern University, Graduate student seminar, April 2013
    Infinitesimal Cherednik algebras (handwritten notes)
  • Harvard-MIT, Graduate student seminar in Geometric Representation theory, September 2011
    Category $\mathcal{O}$ at the negative level (pdf notes)
  • MIT, Infinite Dimensional Algebra Seminar, March 2010
    Ding-Iohara algebras and their action on the K-theory of the Hilbert scheme (handwritten notes)
  • Clay Mathematics Institute, Workshop "Macdonald Polynomials and Geometry", March 2010
    Gelfand-Tsetlin bases via Laumon spaces (handwritten notes)