I am enthusiastic about linking different fields of mathematics and about developing algebraic techniques to solve problems arising in the sciences. My research addresses Applied Algebraic Analysis and Topological Data Analysis.
Algebraic Analysis investigates systems of linear partial differential equations by algebraic methods. It elegantly combines methods from Algebraic Geometry, Algebraic Topology, Category Theory, and Complex Analysis. Many special functions in the sciences are encoded by a holonomic annihilating ideal in the Weyl algebra D and can be investigated by means of D-modules. In this area, I focus on computational aspects and applications - among others, the maximum likelihood estimation of discrete statistical models for the inference of data. At my (virtual) office door, you can have a look at my poster about Algebraic Analysis and Applications.
Topological Data Analysis analyzes the shape of data by topological methods. It has concrete applications in neurosciences and machine learning, for instance. One main tool is persistent homology. It associates persistence modules and so called barcodes to data, from which one easily reads topological features. Behind the scenes, algebraic invariants keep the machinery running. My emphasis in this area lies on the development of stable invariants for multipersistence modules.
- Stable Invariantsfor Multipersistence Modules arising from Hierarchical Stabilization (with Wojciech Chachólski and René Corbet). In preparation.
- Nonlinear Algebra and Applications (with Paul Breiding, Türkü Ö. Çelik, Timothy Duff, Alexander Heaton, Aida Maraj, Lorenzo Venturello, and Oğuzhan Yürük). Preprint arXiv:2103.16300, 2021. Invited expository article by Numerical Algebra, Control and Optimization. Submitted.
- Combinatorial Differential Algebra of xp (with Rida Ait El Manssour). Preprint arXiv:2102.03182, 2021. Submitted to the special issue of the Journal of Symbolic Computation on the occasion of MEGA 2021.
- Maximum Likelihood Estimation from a Tropical and a Bernstein-Sato Perspective (with Robin van der Veer). Preprint arXiv:2101.03570, 2021. Submitted to International Mathematics Research Notices.
- Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument (with Paul Görlach and Christian Lehn). Beiträge zur Algebra und Geometrie 62:397-427, 2021. Final version also available at arXiv:2005.06162.
- A Musical Review of the Empty Set, fun with(out) music and maths.
- Algebraic Analysis of Rotation Data (with Michael Adamer, András Lőrincz, and Bernd Sturmfels). Algebraic Statistics 11(2):189-211, 2020.
- D-Modules and Holonomic Functions (with Bernd Sturmfels). Preprint arXiv:1910.01395, 2019. To be published in the volume Varieties, polyhedra, computation of EMS Series of Congress Reports.
- Topological computation of Stokes matrices of some weighted projective lines. Manuscripta mathematica 164(3):327-347, 2021.
|07/2019 - today||Postdoctoral researcher|
Research Group in Nonlinear Algebra of Prof. Bernd Sturmfels
Max Planck Institute for Mathematics in the Sciences, Leipzig
|05/2019||Defense of the doctoral thesis|
Title: Topological Computation of Stokes Data of Weighted Projective Lines
Partially supported by the German Academic Scholarship Foundation
Supervisor: Prof. Maco Hien, Advisor: Prof. Maxim Smirnov
University of Augsburg
|09/2015 - 06/2019||Scientific assistant of Prof. Marco Hien|
University of Augsburg
|07/2015||Master's degree in Mathematics within TopMath|
University of Augsburg/Technical University of Munich
Please find a more detailed CV, an overview of recent and upcoming talks, and more details about me on my personal website.
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