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mathias.sonnleitner[at]jku.at
math.firstletteroflastname[at]posteo.net
About me
About me
I am an Erwin Schrödinger postdoctoral fellow at the Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz. Previously, I was a postdoc at University of Alberta, University of Münster and University of Passau.
I obtained my doctoral degree in 2022 from University of Passau after extended stays at Johannes Kepler University Linz and University of Graz.
My research interests lie in fields related to functional analysis, geometry and probability theory such as:
Asymptotic Geometric Analysis, Geometric Probability, Information-based Complexity, Stochastic Geometry,...
2025-04 - now: Erwin Schrödinger fellow at Johannes Kepler University Linz hosted by Friedrich Pillichshammer
2024-09 - 2025-03: Erwin Schrödinger fellow at University of Alberta hosted by Alexander Litvak
2024-04 - 2024-08: Erwin Schrödinger fellow at University of Münster hosted by Zakhar Kabluchko
2022-05 - 2024-03: Postdoctoral researcher at University of Passau in group of Joscha Prochno
2022-05: Dr. rer. nat. (~Phd) in Mathematics at University of Passau supervised by Joscha Prochno & Aicke Hinrichs
2019-10 - 2022-04: Research assistant at Johannes Kepler University Linz and University of Graz (alternating stays)
2015-10 - 2019-09: Dipl.-Ing. (~MSc.) in Mathematics at Johannes Kepler University Linz
Publications and Preprints
Publications and Preprints
16. A limit theorem for Hausdorff approximation by random inscribed polytopes.
15. with A. E. Litvak and T. Szczepanski: Minimal dispersion on the sphere.
14. with Z. Kabluchko: Strange shadows of ℓp-balls. Israel J. Math., accepted.
13. with J. Prochno and J. Vybı́ral: Entropy numbers of finite-dimensional Lorentz space embeddings. Studia Math., 283:105-131, 2025.
arXiv:2404.06058 | doi.org/10.4064/sm240409-15-2
12. with J. Prochno, C. Schütt and E. M. Werner: Random approximation of convex bodies in Hausdorff distance. Math. Ann., 392:4525-4542, 2025..
arXiv:2404.02870 | doi.org/10.1007/s00208-025-03186-7
11. with M. Ullrich: On the power of iid information for linear approximation. JANA, 1:88-126, 2023.
arXiv:2310.12740 | doi.org/10.30970/ana.2023.1.88
10. with C. Thäle: A note on critical intersections of classical and Schatten p-balls. Random Matrices Theory Appl., 14(2), Article 2550006, 2025.
arXiv:2308.10635 | doi.org/10.1142/S2010326325500066
9. Unlocking Your Bike the Easy Way. Amer. Math. Monthly, 131(7):581-594, 2024.
arXiv:2308.10321 | doi.org/10.1080/00029890.2024.2346070
8. with Z. Kabluchko and J. Prochno: A probabilistic approach to Lorentz balls. J. Funct. Anal., 288(1), Article 110682, 2025.
arXiv:2303.04728 | doi.org/10.1016/j.jfa.2024.110682
7. with A. Hinrichs and J. Prochno: Random sections of ℓp -ellipsoids, optimal recovery and Gelfand numbers of diagonal operators. J. App. Theory, 293, Article 105919, 2023.
arXiv:2109.14504 | doi.org/10.1016/j.jat.2023.105919
6. with D. Krieg: Function recovery on manifolds using scattered data. J. App. Theory, to appear.
arXiv:2109.04106 | doi.org/10.1016/j.jat.2024.106098
5. with D. Krieg and E. Novak: Recovery of Sobolev functions restricted to iid sampling. Math. Comp., 91(338):2715–2738, 2022.
arXiv:2108.02055 | doi.org/10.1090/mcom/3763
4. with F. Pillichshammer: On the relation of the spectral test to isotropic discrepancy and Lq -approximation in Sobolev spaces. J. Complex., 67, Article 101576, 2021.
arXiv:2010.04522 | doi.org/10.1016/j.jco.2021.101576
3. with D. Krieg: Random points are optimal for the approximation of Sobolev functions. IMA J. Numer. Anal., 2023.
arXiv:2009.11275 | doi.org/10.1093/imanum/drad014
2. with A. Baci, Z. Kabluchko, J. Prochno and C. Thäle: Limit theorems for random points in a simplex. J. Appl. Probab., 59(3):685–701, 2022.
arXiv:2005.04911 | doi.org/10.1017/jpr.2021.77
1. with F. Pillichshammer: A note on isotropic discrepancy and spectral test of lattice point sets. J. Complex., 58, Article 101441, 2020.
arXiv:1907.06435 | doi.org/10.1016/j.jco.2019.101441
Theses
The power of random information for numerical approximation and integration, Phd thesis, University of Passau, 2022. nbn-resolving.de/urn:nbn:de:bvb:739-opus4-11305
Discrepancy and Numerical Integration on Spheres, Master's thesis, Johannes Kepler University Linz, 2019. resolver.obvsg.at/urn:nbn:at:at-ubl:1-30468
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