Alexei Stepanenko

PhD student in mathematical analysis

Welcome to my personal website! I am a PhD student at Cardiff University School of Mathematics, supervised by Jonathan Ben-Artzi and Marco Marletta.

E-mail: stepanenkoa@cardiff.ac.uk

Address:
School of Mathematics
Cardiff University
Senghennydd Road
Cardiff CF24 4AG
United Kingdom

Research Interests

Spectral theory, especially:

Publications and preprints

  1. Computing eigenvalues of the Laplacian on rough domains,
    (w/ Frank Rösler) arXiv:2104.09444 (2021)
  2. Bounds for Schrödinger operators on the half-line perturbed by dissipative barriers,
    arXiv:2010.05663 (2020)
  3. Spectral inclusion and pollution for a class of dissipative perturbations,
    arXiv:2006.10097 Journal of Mathematical Physics 62, 013501 (2021)

Additional resources

Slides for Cardiff analysis seminar October 2020.

Image Gallery

Images from past and current research.

Schr&oumldinger operator perturbed by dissipative barrier 1: no background potential Schr&oumldinger operator perturbed by dissipative barrier 2: decaying background potential Schr&oumldinger operator perturbed by dissipative barrier 3: periodic background potential
Enclosures for the limiting essential spectrum Counting zeros of analytic functions in the upper half plane
Bifurcation diagram for the Poincaré section of a damped, driven Duffing oscillator 1 Bifurcation diagram for the Poincaré section of a damped, driven Duffing oscillator 2