News
- 2026The maximal difference theorem for s-numbers is now formalized in Lean 4 and registered in Palomar, the public registry of Lean-verified results.
- 2026New preprint: the approximation numbers are bounded by every s-number sequence, up to a factor e(n+1). This settles questions of Mityagin, Henkin, Carl and Pietsch dating back to 1963.
- 2026Invited survey for Acta Numerica (vol. 35), joint with David Krieg, appeared.
- 2026New article in the Advances in Computational Mathematics on numerics for high-dimensional approximation with random points and sparse grids, joint with J. Eggl and E. Mindlberger.
- 2026New article in the Journal of Machine Learning Research on the approximation power of deep ReLU networks, joint with C. Schneider and J. Vybiral.
- 2026Joined the editorial board of Communications in Mathematics.
- 2026Building the new lecture series Mathematics for Quantum Science 1–3 (from WS 2026).
- 2025Joined the editorial board of the Journal of Machine Learning Research.
About
I am a mathematician at the Johannes Kepler University Linz, working at the interface of numerical analysis, information-based complexity, and high-dimensional probability.
I am a Senior Scientist at both the Institute of Analysis and the Department of Quantum Computing at JKU. I completed my Habilitation in Linz in 2023, after a PhD in Jena under Erich Novak.
My work received the 2021 Joseph F. Traub Prize for Achievement in Information-Based Complexity, awarded for contributions to the numerics and complexity of high-dimensional integration and approximation, and in particular the power of random information.
In 2026 I was invited to write a survey for Acta Numerica (vol. 35), the leading review journal in numerical analysis, which I co-authored with David Krieg. “Approximation of functions: optimal sampling and complexity” draws together a decade of work on sampling recovery and the gap between optimal and random information.
Contact
Address
Dr. Mario Ullrich
Institute of Analysis
Johannes Kepler University Linz
Altenberger Straße 69
4040 Linz, Austria