E-mail:      kozhan {at} math {dot} uu {dot} se

Phone:       +4618-471 3259

Office:      14139, Department of Mathematics (Ångström Laboratory), Uppsala University

Address:     Lägerhyddsvägen 1, 752 37 Uppsala, Sweden

Education and Employment:

  • Associate Professor (Senior Lektor), Uppsala University, Sweden, 08/2019 - present
  • Docent title in Mathematics (Analysis and Probability), 06/2019
  • Assistant Professor (Biträdande Lektor), Uppsala University, Sweden, 08/2015 - 07/2019
  • Post-doctoral Researcher, KTH, Stockholm (Sweden), 08/2013 – 07/2015
  • Hedrick Assistant Professor, UCLA, 09/2010 - 07/2013
  • Ph.D. in Mathematics, with Best Dissertation Prize, Caltech, 09/2006 - 06/2010
    (Advisor: Prof Barry Simon; thesis title: "Asymptotics for orthogonal polynomials, exponentially small perturbations and meromorphic continuations of Herglotz functions")
  • Master's in Mathematics/Statistics, with distinction, Lviv National University (Ukraine), 2005-2006
  • Bachelor's in Mathematics, with distinction, Lviv National University (Ukraine), 2001-2005

Research Interests

  • Spectral Theory
  • Random Matrix Theory
  • Orthogonal Polynomials
  • Scattering Theory


  • R.K., M.Tyaglov, Multiplicative rank-one perturbations of Jacobi matrices and random matrix ensembles, in preparation.
  • R.Killip, R.K., Distribution of zeros of random orthogonal polynomials, in preparation.
  • R.K., F.Štampach, On the asymptotic zero distribution of orthogonal polynomials on the unit circle with varying Verblunsky coefficients, in preparation.
  • M.Duits, B.Fahs, R.K., Global Fluctuations for Multiple Orthogonal Polynomial Ensembles, 45pp, under submission (arXiv:1912.04599).
  • A.I.Aptekarev, R.K., Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class, 20pp, under submission (arXiv:1908.04540).
  • R.K., Spectral and resonance problem for perturbations of periodic Jacobi operators, 42pp, under submission (arXiv:1211.4274v3).
  • R.K., On Gaussian random matrices coupled to the discrete Laplacian, to appear in Oper. Theory Adv. Appl. (2019), Issue "Analysis as a Tool in Mathematical Physics", in memory of Boris Pavlov (editors P.Kurasov, A.Laptev, S.Naboko, and B.Simon)  (arXiv:1801.05749).
  • M.Duits, R.K., Relative Szegő asymptotics for Toeplitz determinants, IMRN, 2019(17) (2019), pp. 5441–5496, (arXiv:1611.01020).
  • R.K., Rank one non-Hermitian perturbations of Hermitian beta-ensembles of random matrices, J. of Statistical Phys. 168(1) (2017), pp. 92-108 (arXiv:1510.04456).
  • R.Killip, R.K., Matrix models and eigenvalue statistics for truncations of classical unitary ensembles of random matrices, Comm. Math. Phys. 349(3) (2017), pp 991-1027 (arXiv:1501.05160).
  • R.K., Finite range perturbations of finite gap Jacobi and CMV operators, Advances in Math. 301 (2016), pp 204-226 (arXiv:1410.7272).
  • R.K., Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices, Comm. Math. Phys. 327 (2014), no. 3, pp.921–950 (arXiv:1210.4627v2).
  • R.K., Jost asymptotics for matrix orthogonal polynomials on the real line, Constr. Approx. 36 (2012), no. 2, pp.267-309 (arXiv:1104.0460v2).
  • R.K., Equivalence classes of block Jacobi matrices, Proc. Amer. Math. Soc. 139 (2011), pp.799-805 (arXiv:0911.1586v2).
  • R.K., Szegő asymptotics for matrix-valued measures with countably many bound states, J. of Approx. Theory, 162, Issue 6 (2010), pp.1211-1224 (arXiv:0910.1975v2).
  • R.K., L1-spectrum of Banach space valued Ornstein–Uhlenbeck operators, Semigroup Forum, Vol.78, no.3(2009), pp.547-553 (arXiv:1210.1287).
  • R.K., Asymptotics of the eigenvalues of two-diagonal Jacobi matrices, Mathematical Notes, 77, no.1-2(2005), pp.283-287 (arXiv:1210.1292).

Research Projects

Here you can find possible projects that I would be interested in working with an interested student (Bachelor, Master, or PhD levels).


Current teaching (Uppsala):


Past teaching (Uppsala):


Past teaching (UCLA):

  • Spring 2013: Calculus of Several Variables - Math32a (students' evaluations: 8.18/9.0)
  • Spring 2013: Partial Differential Equations - Math 136 (students' evaluations: 7.75/9.0)
  • Winter 2013: Calculus of Several Variables - Math32a (students' evaluations: 8.05/9.0)
  • Fall 2012: Calculus of Several Variables - Math32a (students' evaluations: 7.58/9.0)
  • Spring 2012: Complex Analysis - Math132 (students' evaluations: 8.0/9.0)
  • Winter 2012: Calculus of Several Variables - Math32A  (students' evaluations: 7.42/9.0)
  • Fall 2011: Calculus of Several Variables - Math32A (students' evaluations: 7.49/9.0)
  • Fall 2011: Analysis - Math 131A (students' evaluations: 7.06/9.0)
  • Spring 2011: Ordinary Differential Equations - Math 135 (students' evaluations: 7.52/9.0)
  • Spring 2011: Partial Differential Equations - Math 136 (students' evaluations: 7.08/9.0)
  • Winter 2011: Linear Algebra and Applications - Math 33A (students' evaluations: 5.90/9.0)
  • Fall 2010: Analysis - Math 131A (students' evaluations: 5.84/9.0)


Last updated: September 2019