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Vasily Pestun Permanent Professor

My research is in the field of mathematical physics, quantum field theory and string theory. I explore non-perturbative methods to solve strongly interacting quantum field theories.

Other publications

  • Tensor network language model
    V. Pestun, Y. Vlassopoulos 2017-10-27
  • Language as a matrix product state
    V. Pestun, J.Terilla, Y. Vlassopoulos 2017-11-04
  • Invited conference talks

    Invited department talks


    Mathematics in Paris

    Physics in Paris


    Teaching Experience

    • Teaching Assistant at Princeton University 2004-2007
      • PHY 305 Advanced Quantum Mechanics II
      • PHY 106 Advanced Electromagnetism
      • PHY 105 Advance Mechanics
      • PHY 406 Nuclear and Elementary Particle Physics
      • PHY 510 Relativistic Quantum Field Theory II (graduate)
      • PHY 523 General Relativity (graduate)
    • 2001-2003 ITEP-ITP School on Quantum Fields and Strings, Kiev
    • 2003 ITEP Winter School, Moscow
    • 1998 & 1999 International Physics Olympiad Russian team coach
    • 1998-2000 Board of the National Russian Physics Olympiad
    • 1998-1999 Board of the International Physics Soros Olympiad

    Professional service

    • Letters in Mathematical Physics
    Referee for
    • ZBMath
    • Communications in Mathematical Physics
    • Letters in Mathematical Physics
    • Journal of High Energy Physics
    • AMS Mathematical Reviews
    • Physical Review D


    Quantum Field Theory is a universal framework to address quantum physical systems with infinitely many interacting degrees of freedom, applicable both at the level of fundamental interactions, such as the subnuclear physics of quarks and gluons and at the phenomenological level such as the physics of quantum fluids and superconductivity. Traditionally, weakly interacting quantum field theory is formulated as a perturbative deformation of the linear theory of freely propagating quantum waves or particles with interactions described by Feynman diagrams. For strongly non-linear quantum field theories the method of Feynman diagrams is not adequate. The main goal of this proposal is to develop novel tools and techniques to address strongly non-linear quantum field theories. To achieve this goal we will search for hidden algebraic structures in quantum field theories that will lead to efficient algorithms to compute physical observables of interest. In particular we identify non-linear quantum field theories with exactly solvable sectors of physical observables. In this project we will focus on three objectives: - build general theory of localization in supersymmetric Yang-Mills theory for arbitrary geometrical backgrounds - find all realizations of symplectic and supersymplectic completely integrable systems in gauge theories - construct finite supersymmetric Yang-Mills theory in terms of the algebra of locally supersymmetric loop observables for maximally supersymmetric gauge theory The realization of the above objectives will uncover hidden quantum algebraic structures and consequently will bring ground-breaking results in our knowledge of quantum field theories and the fundamental interactions.

    Alexander Alexandrov, Hisayoshi Muraki, Chaiho Rim, From minimal gravity to open intersection theory (2019); Indexed Apr 15, 2019

    Jihwan Oh and Junya Yagi, Chiral algebras from \Omega-deformation (2019); Indexed Mar 26, 2019

    Chris Elliott and Vasily Pestun, Multiplicative Hitchin Systems and Supersymmetric Gauge Theory (2018); Indexed Dec 13, 2018

    Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky et al., Towards a full solution of the large N double-scaled SYK model (2018); Indexed Nov 6, 2018

    Rouven Frassek and Vasily Pestun, A family of GL(r) multiplicative Higgs bundles on rational base (2018); Indexed Aug 2, 2018

    A. Alexandrov, G. Chapuy, B. Eynard and J. Harnad, Weighted Hurwitz numbers and topological recursion (2018)
    by the ERC Starting Grant no. 335739, Quantum ...; Indexed Jun 26, 2018

    Chris Elliott and Pavel Safronov, Topological twists of supersymmetric algebras of observables (2018); Indexed May 28, 2018

    Peter Koroteev, A-type Quiver Varieties and ADHM Moduli Spaces (2018); Indexed May 2, 2018

    Peter Koroteev, Anton M. Zeitlin, qKZ/tRS Duality via Quantum K-Theoretic Counts (2018); Indexed Feb 13, 2018

    Anindya Dey, Peter Koroteev, Good IR Duals of Bad Quiver Theories (2017); Indexed Dec 17, 2017

    A. Gorsky, A. Milekhin, N. Sopenko, Bands and gaps in Nekrasov partition function (2017); Indexed Dec 8, 2017

    Owen Gwilliam and Brian Williams, The holomorphic bosonic string (2017); Indexed Nov 15, 2017

    Vasily Pestun, John Terilla, Yiannis Vlassopoulos, Language as a matrix product state (2017); Indexed Nov 4, 2017

    Vasily Pestun, Yiannis Vlassopoulos, Tensor network language model (2017); Indexed Oct 27, 2017

    Chris Elliott and Philsang Yoo, A Physical Origin for Singular Support Conditions in Geometric Langlands Theory (2017); Indexed Jul 5, 2017

    Taro Kimura, Vasily Pestun, Fractional quiver W-algebras (2017); Indexed May 12, 2017

    Michele Cirafici, Quivers, Line Defects and Framed BPS Invariants (2017); Indexed Mar 19, 2017

    Michele Cirafici, Michele Del Zotto, Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I (2017); Indexed Mar 14, 2017

    Chris Elliott, Brian Williams, Philsang Yoo, Asymptotic Freedom in the BV Formalism (2017); Indexed Feb 20, 2017

    A. Alexandrov, G. Chapuy, B. Eynard et al., Weighted Hurwitz numbers and topological recursion: an overview (2016); Indexed Oct 28, 2016

    Taro Kimura and Vasily Pestun, Quiver elliptic W-algebras (2016); Indexed Aug 16, 2016

    Vasily Pestun, Review of localization in geometry (2016); Indexed Aug 9, 2016

    Vasily Pestun and Maxim Zabzine, Introduction to localization in quantum field theory (2016); Indexed Aug 9, 2016

    Taro Kimura and Vasily Pestun, Quiver W-algebras (2015); Indexed Dec 28, 2015

    Li Qiao and Jian-Rong Li, Three-term recurrence relations of minimal affinizations of type $G_2$ (2014); Indexed Dec 12, 2014