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I am working on quantitative mixing in partially hyperbolic dynamics, the regularity of solutions to cohomological equations, and associated group actions.
My research interests also include the Cantor spectrum of discrete Schrödinger operators and the semiclassical asymptotics of solutions to difference equations in the complex plane.
Publications
Publications
Cohomological equation in anisotropic spaces and analytic regularity of its solutions, in preparation.
Double exponential mixing for $\mathbb{Z}^k-$actions by ergodic toral automorphisms and perturbations, in preparation.
Double exponential mixing for free semigroup action by Blaschke products on the circle, in preparation.
Difference equations in the complex plane: quasiclassical asymptotics and Berry phase (with A. Fedotov ), Applicable Analysis (2022) 101:1, 274-296, arXiv
The Spectrum and Density of States of the Almost Mathieu Operator with Frequency Represented by a Continued Fraction with Large Elements (with A. Fedotov ), Math Notes (2020) 107, 1040–1045
Semiclassical asymptotics of the spectrum of the subcritical Harper operator (with A. Fedotov ), Mathematical Notes (2018), 104: 6, 948–952
Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial (with A. Fedotov ),
St. Petersburg Math. J. (2018) 29, 363-381Monodromy matrices for Harper equation (with A. Fedotov ), Days on Diffraction St. Petersburg: IEEE (2018), 102-106
The complex WKB method for difference equations in bounded domains (with A. Fedotov ), Journal of Mathematical Sciences (NY) (2017), 224:1 157-169
Berry phase for difference equations (with A. Fedotov ), Days on Diffraction St. Petersburg: IEEE (2017), 113-116
Complex WKB method for difference equations in unbounded domains (with A. Fedotov ), Days on Diffraction St. Petersburg: IEEE (2016), 140-143
Conference Talks
Conference Talks
Workshop “Semiclassical Asymptotics and Nonlocal Elliptic Problems”, RUDN University, online, 2021
Annual International Conference “Days on Diffraction”, Steklov Math Institute, online, 2020
Conference on Spectral Theory and Mathematical Physics, Sirius Center, Sochi, 2020
Conference “Asymptotic Analysis & Spectral Theory”, University Paris-Sud, Orsay, 2019
School “Randomness in Physics and Mathematics”, ZiF, Bielefeld, 2019
Annual International Conference “Days on Diffraction”, Steklov Mathematical Institute, St. Petersburg, 2019
International School “Spectral Function Theory”, Chebyshev Laboratory, St. Petersburg State University, 2019
Research School “Coulomb Gas, Integrability and Painleve’s Equations”, CIRM, Luminy, 2019,
Fourth Russian-Indian Conference in Statistics and Probability, Euler International Mathematical Institute, St. Petersburg, 2019
Nonlinear dynamics and long-time asymptotics, Steklov Mathematical Institute, St. Petersburg, 2019
Stochastic Models II, Euler International Mathematical Institute, St. Petersburg, 2019
Semi-classical and geometric asymptotics in mathematical physics, Laboratoire CPT, Université de Toulon, Toulon, 2018
St. Petersburg Young Researcher Conference in Probability Theory and Mathematical Physics, Steklov Mathematical Institute, 2017
Annual International Conference “Days on Diffraction”, Steklov Mathematical Institute, St. Petersburg, 2017
Spectral Theory, Differential Equations and Probability, Johannes Gutenberg Universität, Mainz, 2016
8th St.Petersburg Conference in Spectral Theory, Euler International Mathematical Institute, St. Petersburg, 2016
Seminar Talks
Seminar Talks
Geometry, Topology and Dynamics Seminar, University of Illinois Chicago, upcoming
Dynamics seminar, University of Chicago, upcoming
Dynamical Systems seminar, Northwestern Univesity, upcoming
Geometry, Dynamics, Topology seminar, University of Michigan, upcoming
Mathematical Physics and Operator Algebras, Michigan State University, East Lansing, 2021
Department of Mathematical Physics Seminar, St. Petersburg State University, 2019
Dynamical Systems Seminar, Higher School of Economics, Moscow, 2019
Department of Mathematical Physics Seminar, St. Petersburg State University, 2018
Chebyshev Lab Student Colloquium, Chebyshev Laboratory, St. Petersburg State University, 2017
St. Petersburg Seminar on Wave Diffraction and Propagation, Steklov Mathematical Institute, St. Petersburg, 2016
Department of Mathematical Physics Seminar, St. Petersburg State University, 2016
Slides, videos, and posters
Slides, videos, and posters
Schetka.mp4Stochastic Models II, Euler International Mathematical Institute, St. Petersburg, 2019 (video by N. Zalesskaya)
Talk_Shchetka_nxn.pdfWorkshop “Semiclassical Asymptotics and Nonlocal Elliptic Problems”, RUDN University, online, 2021
Dirac May 2020.pdfAnnual International Conference “Days on Diffraction”, Steklov Math Institute, online, 2020
Semiclassical_Approximations_for_the_Spectrum_of_the_Critical_and_Subcritical_Harper_Operator.pdfInternational School “Spectral Function Theory”, Chebyshev Laboratory, St. Petersburg State University, 2019
DD-talk.pdfAnnual International Conference “Days on Diffraction”, Steklov Mathematical Institute, St. Petersburg, 2019
Semiclassical_Approximations_for_the_Spectrum_of_the_Subcritical_Harper_Operator-4.pdfResearch School “Coulomb Gas, Integrability and Painleve’s Equations”, CIRM, Luminy, 2019
Slides__School_ZiF_Bielefeld_2019_-4.pdfSchool “Randomness in Physics and Mathematics”, ZiF, Bielefeld, 2019
Shchetka-2018-Toulon.pdfSemi-classical and geometric asymptotics in mathematical physics, Laboratoire CPT, Université de Toulon, Toulon, 2018
DD-2017-Shchetka.pdfAnnual International Conference “Days on Diffraction”, Steklov Mathematical Institute, St. Petersburg, 2017
Shchetka.pdfSpectral Theory, Differential Equations and Probability, Johannes Gutenberg Universität, Mainz, 2016
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