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Currently, I am doing my doctorate under the supervision of Prof. Dr. Ulrich Bauer in his Applied & Computational Topology group at the Technical University of Munich.

I am mainly interested in topological properties of geometric complexes as well as combinatorial homotopy theory in general.


Publications and preprints

  • A Unified View on the Functorial Nerve Theorem and its Variations – with Ulrich Bauer, Michael Kerber, and Alexander Rolle. [preprint] (2022) [poster]
  • Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris–Rips Filtrations – with Ulrich Bauer. Accepted to SoCG 2022. [extended version] [poster]

Invited talks

  • Applied CATS Seminar at the KTH in Stockholm. A Unified View on the Functorial Nerve Theorem and its Variations. April 26, 2022. Slides.

Theses

  • Master’s Thesis (2020): Variations of the Nerve Theorem [poster]
  • Bachelor’s Thesis (2018): Cohomology and the de Rham Isomorphism

Students advised

  • Markus Ruhland (2021, Bachelor’s thesis, jointly with Ulrich Bauer): Homological Algebra in Puppe-exact Categories

Teaching

  • Geometry and Topology for Data Analysis (WS 21/22, Teaching Assistant)
  • Linear Algebra for Informatics (SS 21, exercise session)
  • Mathematics for Physicists 1 – Linear Algebra (WS 18/19, Tutor)
  • Linear Algebra for Informatics (SS 18, Tutor)
  • Mathematics for Physicists 1 – Linear Algebra (WS 17/18, Tutor)
  • Advanced Mathematics 1  (WS 17/18, Tutor)
  • Schnupperstudium Mathefrühling (SS 17, Tutor)

Applets and animations

knot visualization

coordinate systems

untangling a knot

ribbon visualization

plane over a finite field

Contact

E-Mail: fabian@roll.science

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