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
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
Theory of Orthogonal Polynomials
Spectral Theory
Approximation Theory
Random Matrix Theory
R.K., M.Vaktnäs, Zeros of multiple orthogonal polynomials: location and interlacing, 19pp., under submission (arXiv:2503.15122).
R.K., Nikishin systems on the unit circle, 18pp., under submission (arXiv:2410.20813).
R.K., M.Vaktnäs, Laurent Multiple Orthogonal Polynomials on the Unit Circle, 21pp., under submission (arXiv:2410.12094).
R.K., M.Vaktnäs, Christoffel Transform and Multiple Orthogonal Polynomials, 28pp., under submission (arXiv:2407.13946).
R.K., M.Vaktnäs, Determinantal Formulas for Rational Perturbations of Multiple Orthogonality Measures, 22pp., under submission (arXiv:2407.13961).
R.K., Spectral and resonance problem for perturbations of periodic Jacobi operators, 42pp, under submission (arXiv:1211.4274v3).
G.Alpan, R.K., Multiplicative non-Hermitian perturbations of classical β-ensembles, accepted in Random Matrices: Theory and Applications (2025) (arXiv:2308.06627).
R.K., M.Vaktnäs, Szegő recurrence for multiple orthogonal polynomials on the unit circle, Proc. of AMS, 152, 7 (2024), pp.2983-2997 (arXiv:2404.18666).
R.K., M.Tyaglov, A generalized Hermite--Biehler theorem and non-Hermitian perturbations of Jacobi matrices, J. of Mathematical Analysis and Applications, Vol. 536(2) (2024), 128241. (arXiv:2302.07018).
G.Alpan, R.K., Hermitian and non-Hermitian perturbations of chiral Gaussian β-ensembles, J. Math. Phys. 63, 043505 (2022) (arXiv:2109.13982).
M.Duits, B.Fahs, R.K., Global Fluctuations for Multiple Orthogonal Polynomial Ensembles, J. of Functional Analysis 281(5) (2021) (arXiv:1912.04599).
A.I.Aptekarev, R.K., Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class, J. Approx. Theory 255 (2020), 105409, 21 pp. (arXiv:1908.04540).
R.K., On Gaussian random matrices coupled to the discrete Laplacian, in Oper. Theory Adv. Appl. (2020), 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, https://doi.org/10.1093/imrn/rnx266 (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).
R.K., M.Vaktnäs, Generalized Hermite-Pade problem on the unit circle.
R.Killip, R.K., Distribution of zeros of random orthogonal polynomials, in preparation.
R.K., F.Štampach, Ratio asymptotics and zero density of orthogonal polynomials with varying Verblunsky coefficients, in preparation.
2022—present: Co-supervisor for PhD project, David Meadon, Uppsala University
2021—present: Supervisor for PhD project, Marcus Vaktnäs, Uppsala University
2022: Supervisor for Bachelor project “Gap probabilities in random matrix theory”, Oskar Bäcklin, Uppsala University
2021: Supervisor for Master Project “Multiple orthogonal polynomials and modifications of spectral measures”, Marcus Vaktnäs, Uppsala University
2021: Subject reader for Bachelor project “Hilbert spaces and the spectral theorem”, Felicia Lapinski, Uppsala University
2020--2022: Supervisor for Postdoc project “Resonances in random matrix theory”, Gökalp Alpan, Uppsala University (Vergstiftelsen Grant)
Here you can find potential projects that I would be interested in working with an interested student (Bachelor, Master, or PhD levels).
Current teaching (Uppsala):
Spring Q3-4 2025: Geometry and Calculus II - 1MA188
Spring Q3-4 2025: Flervariabelanalys - 1MA016
Past teaching (Uppsala):
Fall Q2 2024: Transform Methods - 1MA034 (students' evaluations: 4.0/5.0)
Spring Q3-4 2024: Geometry and Calculus II - 1MA188 (students' evaluations: 4.8/5.0)
Spring Q3-4 2024: Flervariabelanalys - 1MA016
Fall Q2 2023: Transform Methods - 1MA034 (students' evaluations: 3.6/5.0)
Spring Q3-4 2023: Geometry and Calculus II - 1MA188 (students' evaluations: 4.7/5.0)
Spring Q3-4 2023: Flervariabelanalys - 1MA016
Spring Q3-4 2022: Geometry and Calculus II - 1MA188 (students' evaluations: 4.6/5.0)
Spring Q3-4 2022: Flervariabelanalys - 1MA016
Spring Q3-4 2021: Geometry and Calculus II - 1MA188 (students' evaluations: 4.5/5.0)
Spring Q3-4 2021: Flervariabelanalys - 1MA016
Spring Q3-4 2020: Geometry and Calculus II - 1MA188 (students' evaluations: 4.7/5.0)
Fall Q2 2019: Transform Methods - 1MA034 (students' evaluations: 4.0/5.0)
Fall Q1 2018: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.3/5.0)
Spring Q3-4 2018: Analysis for PhD students
Fall Q1 2017: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.7/5.0)
Spring Q3-4 2017: Geometry and Calculus II - 1MA188 (students' evaluations: 4.6/5.0)
Fall Q1 2016: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.7/5.0)
Spring Q3-4 2016: Geometry and Calculus II - 1MA188 (students' evaluations: 5.0/5.0)
Fall Q1 2015: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.8/5.0)
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)
My
CV
Last updated:
March 2025