Research areas
Asymptotic analysis of orthogonal polynomials, determinants, and multiple integrals which appear, in particular, in random matrix theory and integrable models.

Spectral properties of quasiperiodic Schroedinger operators.
Teaching
Measure and Integration, autumn 2011, 2012, 2013, 2014, 2016, 2017, 2018.

Distribution Theory, spring 2012.

Metric Spaces and Topology, spring 2013, 2014, 2015.

Probability, spring 2017.

Random Matrices, spring 2017.

Analysis I, spring 2018, 2019.

Fourier Analysis and Distributions, spring 2021.

Selected publications:
Toeplitz, Hankel determinants, orthogonal polynomials, random matrices, integrable models.


"Sine-kernel determinant on two large intervals'' (with B. Fahs), [http://arxiv.org, \\ arXiv:2003.08136]

"Toeplitz determinants with merging singularities'' (with T. Claeys), Duke Math. J. 164 (2015) 2897--2987

''Asymptotics of Toeplitz, Hankel, and Toeplitz Hankel determinants with Fisher-Hartwig singularities'' (with P. Deift and A. Its), Ann. of Math. 174 (2011) 1243--1299

"Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant", Duke Math. J. 139 (2007) 581--619

"Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle", Int. Math. Res. Notices 2004 (2004) 1249--1272
Quasiperiodic operators
"Critical almost Mathieu operator: Hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum'' (with S. Jitomirskaya) [http://arxiv.org, arXiv:1909.04429]

"Central spectral gaps of the almost Mathieu operator'', Commun. Math. Phys. 351 (2017), 419--439

''Continuity of the measure of the spectrum for discrete quasiperiodic operators'' (with S. Jitomirskaya), Math. Res. Lett. 9 (2002) 413--422

''Bloch electron in a magnetic field and the Ising model'', Phys. Rev. Lett. 85 (2000) 4920--4923