Publications

• R.K., M.Vaktnäs, Multiple orthogonal polynomials and modifications of spectral measures, in preparation.

• 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.

• R.K., M.Vaktnäs, The Szegő recurrence for multiple orthogonal polynomials on the unit circle, under submission.

• G.Alpan, R.K., Multiplicative non-Hermitian perturbations of classical β-ensembles, under submission (arXiv:2308.06627).

• R.K., M.Tyaglov, A generalized Hermite--Biehler theorem and non-Hermitian perturbations of Jacobi matrices, under submission (arXiv:2302.07018).

• R.K., Spectral and resonance problem for perturbations of periodic Jacobi operators, 42pp, under submission (arXiv:1211.4274v3).

• 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).

Supervision

• 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).

Teaching

Current teaching (Uppsala):

• None

 Past teaching (Uppsala):

• Quarters 3-4, 2021/2022: Geometry and Calculus II - 1MA188 (students' evaluations: 4.6/5.0)

• Quarters 3-4, 2021/2022: Flervariabelanalys - 1MA016

• Quarters 3-4, 2020/2021: Geometry and Calculus II - 1MA188 (students' evaluations: 4.5/5.0)

• Quarters 3-4, 2020/2021: Flervariabelanalys - 1MA016

• Quarter 3-4, 2019/2020: Geometry and Calculus II - 1MA188 (students' evaluations: 4.7/5.0)

• Quarter 2, 2019/2020: Transform Methods - 1MA034 (students' evaluations: 4.0/5.0)

• Quarter 2, 2018/2019: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.7/5.0)

• Quarter 1, 2018/2019: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.3/5.0)

• Quarter 3-4, 2017/2018: Analysis for PhD students

• Quarter 2, 2017/2018: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.7/5.0)

• Quarter 3-4, 2016/2017: Geometry and Calculus II - 1MA188 (students' evaluations: 4.6/5.0)

• Quarter 2, 2016/2017: Ordinary Differential Equations I - 1MA032 (students' evaluations: 4.7/5.0)

• Quarter 3-4, 2015/2016: Geometry and Calculus II - 1MA188 (students' evaluations: 5.0/5.0)

• Quarter 2, 2015/2016: 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: August 2023