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<head>
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<title>Alexei Stepanenko</title>
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<body>
<h1>Alexei Stepanenko</h1>
<p class = "site-description">Research associate in mathematics of information</p>
<img src="WebCropped.jpg" width="250" align = "right" />
Welcome to my personal website!
I am a research associate at <a href="https://www.damtp.cam.ac.uk/">DAMTP, University of Cambridge</a>.
Prior to this, I was a research associate at <a href="https://www.cardiff.ac.uk/mathematics">Cardiff University School of Mathematics</a> and a visiting postdoctoral research fellow at the Centre for Mathematical Sciences, University of Cambridge, mentored by <a href="http://www.damtp.cam.ac.uk/research/afha/anders/">Anders Hansen.</a>
I undertook my PhD at Cardiff University, supervised by <a href="https://jbenartzi.github.io/">Jonathan Ben-Artzi</a> and
<a href="http://www.cardiffmaths.co.uk/marco/">Marco Marletta</a>. <br />
<br />
In the academic year 2022-2023, I organised the <a href="https://jbenartzi.github.io/seminars.html">Cardiff Analysis Seminar</a> and the Cardiff <a href="https://alexeistepa.github.io/mathdl">Mathematics of Deep Learning</a> reading group.
<br />
<br />
<strong> E-mail: </strong> <a href="mailto:as3304@cam.ac.uk" target="_top">alexei.stepa@gmail.com</a> <br />
<br />
<h2> Research Interests</h2>
<ul>
<li> Approximation theory and foundations of computation, especially in the context of PDEs and spectral theory. </li>
<li> Mathematics of deep learning, especially links with PDEs (e.g. Physics-Informed Neural Networks).</li>
<li> Koopman operator learning.</li>
</ul>
<h2> Publications and preprints</h2>
<ol reversed>
<li> Lieb-Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line, <br />
(w/ Leonid Golinskii) <a href = "https://arxiv.org/abs/2111.09629">arXiv:2111.09629</a>, Accepted in <i>Joural of Spectral Theory</i> (2024) </li>
<li> Computing eigenvalues of the Laplacian on rough domains, <br />
(w/ Frank Rösler) <a href = "https://arxiv.org/abs/2104.09444">arXiv:2104.09444</a>, Published online in <i>Mathematics of Computation</i> (2023)</li>
<li> Bounds for Schrödinger operators on the half-line perturbed by dissipative barriers, <br />
<a href = "https://arxiv.org/abs/2010.05663">arXiv:2010.05663</a>, <i>Integral Equations and Operator Theory 93, 60</i> (2021) </li>
<li> Spectral inclusion and pollution for a class of dissipative perturbations, <br />
<a href = "https://arxiv.org/abs/2006.10097">arXiv:2006.10097</a>,
<i>Journal of Mathematical Physics 62, 013501</i> (2021) </li>
</ol>
<h2> Image Gallery </h2>
Images from past and current research. <br />
<br />
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<li><a href="https://github.com/alexeistepa">github.com/alexeistepa</a></li>
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