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mathias.sonnleitner[at]uni-muenster.de
math.firstletteroflastname[at]posteo.net
About me
About me
I am a Postdoc at University of Münster (group of Martin Huesmann) and University of Bielefeld (group of Matthias Erbar) and member of the DFG Priority Programme Random Geometric Systems.
My research focuses on the structure of random point sets and the geometry of high-dimensional convex bodies. As such, my interests lie in fields related to functional analysis, geometry and probability theory, These include: Asymptotic Geometric Analysis, Information-based Complexity, Random Matrix Theory and Stochastic Geometry, among others.
2025 Oct - now: Postdoc 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 Johannes Kepler University Linz and University of Graz, awarded 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
17. with M. Reitzner: Central limit theorems for random boundary polytopes.
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
Academic Service
Academic Service
Associate Editor at Journal of Complexity (JoC)
Reviewed for Constr. App., J. Complexity, Math. Comp., Math. Nachr., Math. Reviews, MCQMC Proc.
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