My research addresses 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 and can be investigated by means of D-modules. In this area, I focus on computational aspects and applications – among others, maximum likelihood estimation of statistical models.
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 datasets, from which one easily reads topological features. Behind the scenes, algebraic structure theorems keep the machinery running. My emphasis in this area lies on advancing the algebraic tools.
- Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument (with Paul Görlach and Christian Lehn). arXiv:2005.06162 [math.AG], submitted to Beiträge zur Algebra und Geometrie.
- 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). arXiv:1912.00396 [math.ST], to appear in Algebraic Statistics, issue 11:2.
- D-Modules and Holonomic Functions (with Bernd Sturmfels). arXiv:1910.01395 [math.AG].
- Topological Computation of the Stokes Matrices of the Weighted Projective Line P(1,3), arXiv:1810.10954 [math.AG]. An extended version Topological computation of Stokes matrices of some weighted projective lines to be published in Manuscripta Mathematica, Springer, 2020, DOI: 10.1007/s00229-020-01193-3.
My current collaborators include:
- Valeria Bertini (TU Chemnitz, Germany)
- René Corbet (KTH Stockholm, Sweden)
- Wojciech Chachólski (KTH Stockholm, Sweden)
- Joscha Diehl (University of Greifswald, Germany)
- Paul Görlach (TU Chemnitz, Germany)
- Christian Lehn (TU Chemnitz, Germany)
- Robin van der Veer (KU Leuven, Belgium)
|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
Here you find a more detailed CV.