About me

I recently obtained a PhD at the NUMA research unit of KU Leuven’s Department of Computer Science. I worked on ‘The Lanczos Tau Method for Time-Delay Systems’ under the supervision of Wim Michiels.

My research focuses on developing numerical methods for infinite-dimensional dynamical systems, particularly those governed by delay and functional differential equations. I work at the intersection of approximation theory, numerical analysis, and dynamical systems theory, with an increasing interest in computational methods for nonlinear dynamics, including the numerical discovery of attractors and the corresponding basins of attraction of infinite-dimensional systems. Whilst my work primarily involves theoretical and computational aspects of these methods, the questions and problems they aim to solve are inspired by applications in engineering and the life sciences.

If you want to know more about my research, or for any other professional or personal inquiries, you can always contact me via email or XMPP on ‘my first name’@eprovst.net.

Works

Below is a list of my scientific output with links to preprints and slides. You can find my full CV here.

Publications and preprints

• P., ‘Lanczos tau methods for time-delay systems: Approximation of system and its H²-norm’, PhD thesis (2026, KU Leuven). [text]
• P. and Wim Michiels, ‘Computing and optimizing the H²-norm of delay differential algebraic systems’. [preprint]
• P. and Wim Michiels, ‘Accelerated H²-norm approximation for time-delay systems with discrete delays’, IFAC-PapersOnLine, 59/11 (2025), 93–8. Presented at the 19^th IFAC Workshop on Time-Delay Systems. [eprint (open access)]
• P. and Wim Michiels, ‘The Lanczos tau framework for time-delay systems: Padé approximation and collocation revisited’, SIAM Journal on Numerical Analysis, 62/6 (2024), 2529–48. [eprint, preprint]

Talks and seminars

Basins of attraction of FDEs

• Contributed talk, 15^th AIMS Conference, Athens, Greece (July 2026). [slides]
• Internal seminar, NUMA research unit, KU Leuven, Leuven, Belgium (November 2025). [slides]

Lanczos tau methods for DD(A)Es

• Invited talk, BeNeLux Mathematical Congress 2026, Antwerp, Belgium (April 2026). [slides]
• Invited talk, 19^th IFAC Workshop on Time-Delay Systems, Gif-sur-Yvette, France (July 2025). [slides]
• Internal seminar, NUMA research unit, KU Leuven, Leuven, Belgium (December 2024). [slides]
• Invited talk, 18^th IFAC Workshop on Time-Delay Systems, Udine, Italy (September 2024). [slides]
• Poster, 6^e Journées Approximation, Lille, France (May 2024). [poster]
• Internal seminar, NUMA research unit, KU Leuven, Leuven, Belgium (March 2024). [slides]
• Contributed talk, 42^nd Benelux Meeting on Systems and Control, Elspeet, The Netherlands (March 2023). [slides]

Domain colouring

Somewhat loosely related to my scientific activities I also ended up getting intrigued by domain colouring, a way to visualize complex functions. This resulted in the development of the Julia packages Domain­Coloring.jl and Complex­Toys.jl. Of note in the method used in these packages is the use of an analytical sweep through the Oklab colour space, resulting in far fewer artefacts and false representations than the usual HSV hue sweep.

The figure shows the fifth diagonal Padé approximant of e^−s as appears in the transfer function when approximating a time-delay system using a Lanczos tau method truncating in the Legendre basis.