Research
Research Interests
- Stochastich (partial) differential equations
- Regularity theory
- Weighted function spaces
- Functional analysis
- Numerics for stochastic differential equations
- Neural networks
My research lies in the analysis of partial and stochastic partial differential equations (PDEs and SPDEs), with a particular focus on questions of well-posedness and regularity. Broadly speaking, I study when such equations admit unique solutions, how the different terms in the equation influence the behaviour of those solutions, and how much irregularity in the data, coefficients, and nonlinearities can still be allowed.
SPDEs arise naturally in many areas of science and engineering, including fluid dynamics, diffusion processes, filtering theory, and mathematical finance. A central challenge in their analysis is the development of robust linear theories that can later be used to treat nonlinear problems. One key concept in this context is stochastic maximal regularity, which provides a powerful framework for obtaining sharp existence, uniqueness, and regularity results.
A particular emphasis of my work is on SPDEs posed on domains with singular boundaries, such as corners, edges, and conic points. While such geometries occur naturally in applications, they create substantial mathematical difficulties: standard Sobolev regularity fails, as solutions typically develop singular behaviour near the boundary or at geometric singularities. To address this, I work with weighted function spaces that capture these local effects in a precise way.
In recent work, I developed a regularity theory for the Dirichlet Laplacian on conic domains by proving bounded holomorphic functional calculus results in weighted Lp-spaces. These results substantially strengthen the deterministic theory and provide a foundation for maximal regularity methods for nonlinear SPDEs on non-smooth domains.
Publications / Preprints
| 2. The H∞-calculus for the Dirichlet-Laplacian on conical domains. (with P. A. Cioica-Licht, E. Lorist) Submitted. [arXiv:2509.09519] |
| 1. Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations. (with P. A. Cioica-Licht, M. Hutzenthaler) To appear in Communications in Mathematical Sciences. [arXiv:2205.14398] |
Curriculum Vitae
Professional experience
| Since 11/2021 | Research Assistant (PhD Candidate), Stochastics Group, Institute of Mathematics, University of Kassel, Germany |
| 10/2020 – 10/2021 | Teaching Assistant, Stochastic Analysis Group, Faculty of Mathematics, University of Duisburg-Essen, Germany |
Education
| Since 11/2021 | PhD student at University of Kassel Dissertation (working title): Differential operators on domains with corners and edges and applications to SPDE Advisor: Dr. Petru A. Cioica-Licht |
| 2019 – 2021 | Master’s Program in Mathematics (Major) and Business Administration (Minor), University of Duisburg-Essen Thesis: Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations Advisor: Prof. Dr. Martin Hutzenthaler |
| 2015 – 2018 | Bachelor’s Program in Mathematics (Major) and Business Administration (Minor), Ulm University Thesis: Advanced container stacking strategies Advisor: Prof. Dr. Henning Bruhn-Fujimoto |
| 2024 | DAAD-Scholarship for a 2 months research stay at Delft University of Technology, the Netherlands |
| 2022 | Best thesis award 2021 of the University of Duisburg-Essen, Mathematics Section |
| 01/2025 | PDE Seminar, Delft University of Technology | The H∞-calculus of the Dirichlet-Laplacian on a wedge |
| 12/2024 | Analysis Seminar, University of Kassel | The stochastic heat equation and the Dirichlet-Laplacian on a wedge |
| 05/2022 | Stochastic Analysis Seminar, University of Duisburg-Essen | Neural networks overcome the curse of dimensionality in the numerical approximation for semilinear PDE |
| 04/2025 | Analysis and Probability in Infinite Dimensions, Bad Herrenalb | Poster: H∞-Calculus for differential operators in domains with corners and edges |
| 03/2025 | Maximal Regularity Methods in Mathematical Fluid Mechanics, Frankenstein | Talk: SPDEs on non-smooth domains: An operator theoretic perspective |
| 11/2025 | Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis, Oberwolfach |
| 06/2025 | Stochastic Partial Differential Equations in Critical Spaces, Oberwolfach |
| 07/2024 | SPDEs below sealevel, Delft |
| 05/2024 | SPDEvent III, Bielefeld |
| 08/2023 | 18th PhD Student Convent of Stochastics, Heidelberg |
| 07/2023 | SPDEvent II, Bielefeld |
| 04/2023 | 16th German Probability and Statistics Days, Essen |
| 09/2022 | Westphalian Stochastics Days, Paderborn |
| 09/2024 - 10/2024 | Delft University of Technology, the Netherlands Host: Prof. Dr. Mark C. Veraar |
| Summer 2025 | Teaching Assistant for the course Biometrics: Statistics for Biologists (Dr. Petru A. Cioica-Licht), University of Kassel |
| Winter 2024 | Teaching Assistant for the course Stochastic Differential Equations (Dr. Markus Antoni), University of Kassel |
| Winter 2025, 2024, 2023, 2022 | Teaching Assistant for the course Measure and Probability Theory (Dr. Petru A. Cioica-Licht), University of Kassel |
| Summer 2023, 2022 | Teaching Assistant for the course Stochastic Processes (Dr. Petru A. Cioica-Licht), University of Kassel |
| Summer 2021 | Tutor for the course Probability Theory 1 (Prof. Dr. Martin Hutzenthaler), University of Duisburg-Essen |
| Winter 2020 | Tutor for the course Stochastik (Prof. Dr. Martin Hutzenthaler), University of Duisburg-Essen |