I love to link different fields of mathematics and to developing algebraic techniques to solve problems arising in the sciences. My research addresses Algebraic Analysis, Applied Algebraic Geometry, 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 the medical sciences 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.
- Vector Spaces of Generalized Euler Integrals (with Daniele Agostini, Claudia Fevola, and Simon Telen). In preparation.
- Bayesian Integrals on Toric Varieties (with Michael Borinksy, Bernd Sturmfels, and Simon Telen). Preprint arXiv:2204.06414, 2022. Submitted.
Supplementary material: Juptyer notebook available at mathrepo.mis.mpg.de/BayesianIntegrals
- The Shift-Dimension of Multipersistence Modules (with Wojciech Chachólski and René Corbet). Preprint arXiv:2112.06509, 2021. Submitted.
- Nonlinear Algebra and Applications (with Paul Breiding, Türkü Ö. Çelik, Timothy Duff, Alexander Heaton, Aida Maraj, Lorenzo Venturello, and Oğuzhan Yürük). Numerical Algebra, Control and Optimization, 2021.
- Combinatorial Differential Algebra of xp (with Rida Ait El Manssour). Journal of Symbolic Computation, 114:193-208, 2023. DOI:10.1016/j.jsc.2022.04.010
- Maximum Likelihood Estimation from a Tropical and a Bernstein-Sato Perspective (with Robin van der Veer). International Mathematics Research Notices, rnac016, 2022.
- 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 appear 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.
Together with researchers from MPI MiS, KTH, EPFL, MIT, and the University of Oxford, we run the international consortium AlToGeLiS: Algebra, Topology, and Geometry in the Life Science. Revealing structures of data with algebra, topology, and geometry. We aim to strenghten the collaboration among the institutes and to develop and apply mathematical tools for data science. At the same time, this makes nonlinear maths of data more accessible and visible. Check our website www.altogelis.com to stay tuned about news and announcements.
|09/2021 - 12/2021||Research stay with Prof. Wojciech Chachólski |
Brummer & Partners MathDataLab, KTH Royal Institute of Technology, Stockholm
|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.
I am the Equal Opportunity Representative of MPI MiS. In that role, I support and represent our institute regarding all aspects of Equal Opportunities. Don't hesitate to contact me, our conversations are going to be treated confidentially. You reach me and my deputy, Raffaella Mulas, by e-mail at the following address: eq_op (at) mis.mpg.de
Last update: May 2, 2022