Alexei Stepanenko
Research associate in mathematics of information
Welcome to my personal website!
I am a research associate at DAMTP, University of Cambridge.
Prior to this, I was a research associate at Cardiff University School of Mathematics and a visiting postdoctoral research fellow at the Centre for Mathematical Sciences, University of Cambridge, mentored by Anders Hansen.
I undertook my PhD at Cardiff University, supervised by Jonathan Ben-Artzi and
Marco Marletta.
In the academic year 2022-2023, I organised the Cardiff Analysis Seminar and the Cardiff Mathematics of Deep Learning reading group.
E-mail: alexei.stepa@gmail.com
Research Interests
- Approximation theory and foundations of computation, especially in the context of PDEs and spectral theory.
- Mathematics of deep learning, especially links with PDEs (e.g. Physics-Informed Neural Networks).
- Koopman operator learning.
Publications and preprints
- Lieb-Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line,
(w/ Leonid Golinskii) arXiv:2111.09629, Accepted in Joural of Spectral Theory (2024)
- Computing eigenvalues of the Laplacian on rough domains,
(w/ Frank Rösler) arXiv:2104.09444, Published online in Mathematics of Computation (2023)
- Bounds for Schrödinger operators on the half-line perturbed by dissipative barriers,
arXiv:2010.05663, Integral Equations and Operator Theory 93, 60 (2021)
- Spectral inclusion and pollution for a class of dissipative perturbations,
arXiv:2006.10097,
Journal of Mathematical Physics 62, 013501 (2021)
Image Gallery
Images from past and current research.
