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mathias.sonnleitner[at]uni-muenster.de
math.firstletteroflastname[at]posteo.net
I am a postdoctoral researcher at the Universities of Münster and Bielefeld as well as a member of the Cluster of Excellence Mathematics Münster.
My research lies at the intersection of analysis, probability and geometry. I study the geometry of random point configurations and high-dimensional convex bodies. My research interests include typical properties of random vectors and matrices, random polytopes, discrepancy and recovering functions from random data.
2025 Oct - now: Postdoctoral researcher in joint DFG project at University of Münster (Martin Huesmann) and University of Bielefeld (Matthias Erbar)
2024 - 2025: Erwin Schrödinger fellow (1.5 years) at
University of Münster hosted by Zakhar Kabluchko,
University of Alberta hosted by Alexander Litvak,
Johannes Kepler University Linz hosted by Friedrich Pillichshammer
2022 - 2024: Postdoc at University of Passau in group of Joscha Prochno
2019 - 2022: Dr. rer. nat. (~PhD) in Mathematics supervised by Joscha Prochno & Aicke Hinrichs at University of Graz and Johannes Kepler University Linz, completed at University of Passau
2015 - 2019: BSc. + Dipl.-Ing. (~MSc.) in Mathematics at Johannes Kepler University Linz
Awards and Grants
Awards and Grants
Publications and Preprints
Publications and Preprints
18. Next-order asymptotics for the volume of Schatten balls.
17. with M. Reitzner: Central limit theorems for random boundary polytopes. Bernoulli, 32(4): 3024-3041, 2026.
arXiv:2509.20058 | doi.org/10.3150/26-BEJ1977
16. A limit theorem for Hausdorff approximation by random inscribed polytopes. Proc. Amer. Math. Soc., in press.
arXiv:2508.16442 | doi.org/10.1090/proc/17703
15. with A. E. Litvak and T. Szczepanski: Minimal dispersion on the sphere. Discrete Comput. Geom., 76:1293-1321, 2026.
arXiv:2505.10929 | doi.org/10.1007/s00454-025-00812-8
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 ℓq,1. 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, 305, Article 106098, 2025.
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., 44(3):1346-1371, 2024.
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
Academic Service
Academic Service
Associate Editor at Journal of Complexity (JoC)
Reviewed for Ann. H. Lebesgue, Constr. App., J. Appl. Probab., J. Complexity, Math. Comp., Math. Nachr., Math. Reviews, MCQMC Proc.
Photo Credits: Stefan Steinerberger
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