Prospective PhD applicants with research interests in Analysis are welcome to contact me in advance to discuss potential projects. 

My research centers on orthogonal polynomials and spectral theory, with an emphasis on links between classical analytic methods and modern spectral and probabilistic problems, and applications to random matrix theory, approximation theory, and mathematical physics.

Recently, I have been especially interested in multiple orthogonal polynomials on the unit circle, a developing area with many open and challenging questions.

I welcome discussions with students and colleagues interested in potential research projects or collaborations.

Theory of Orthogonal Polynomials

Classical and modern aspects on the real line, unit circle, including multiple and matrix-valued settings.

Spectral & Operator Theory

Theory of Jacobi, CMV, Toeplitz, Hankel operators.

Applications in Random Matrices, Integrable Probability & Approximation Theory

Eigenvalues of random matrices, Hermite-Pade appoximation, Gaussian quadrature
Bachelor level projects

- Classical orthogonal polynomials and applications
- Numerical experiments and visualization (zeros, eigenvalues)
- Approximating functions using orthogonal polynomials

minimal prerequisites

Master level projects

- Spectral properties of sparse operators
- Random matrix ensembles and limiting eigenvalue distributions 
- Simultaneous rational approximation

accessible projects with clear potential for publishable results

PhD level projects

- Multiple orthogonal polynomials on the real line / the unit circle
- Spectral theory of operators on graphs
- Fluctuations of eigenvalues of random matrices

research at the interface of analysis and neighboring disciplines

  • R. Kozhan
  • Docent, Associate Professor
  • Department of Mathematics Uppsala University
  • Email: kozhan-at-math.uu.se
  • Phone: +46 18-471-32-fifty nine
  • Address: Box 256, SE-751 05, Uppsala, Sweden

Last updated: 01 July 2026

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