# 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 SchrÃ¶dinger 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 SchrÃ¶dinger 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.