I obtained my doctoral degree in mathematics at the Technical University of Munich advised by Ulrich Bauer. During that time, I organized the research seminar of the Applied and Computational Topology group and the TopMath talk series.
My research mainly focuses on topological and combinatorial properties of geometric complexes as well as their use in topological data analysis.
Publications and preprints
- Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theory – with Ulrich Bauer. SoCG 2024. [doi] [full version] [git]
- Topological analysis of 3D digital ovules identifies cellular patterns associated with ovule shape diversity – with Tejasvinee Atul Mody, Alexander Rolle, Nico Stucki, Ulrich Bauer, Kay Schneitz. Development. [doi] [preprint] [git]
- A unified view on the functorial nerve theorem and its variations – with Ulrich Bauer, Michael Kerber, and Alexander Rolle. Expositiones Mathematicae. [doi] [preprint] [poster]
- Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris–Rips Filtrations – with Ulrich Bauer. SoCG 2022. [doi] [extended version] [poster]
Selected talks
- Applied Topology Seminar (AATRN), online. Bridging Persistent Homology and Discrete Morse Theory with Applications to Shape Reconstruction. June 26, 2024. [slides] [recording]
- Munich Data Science Institute (MDSI) research seminar on data science, machine learning and AI topics in Munich, Germany. Applied Topology. December 11, 2023. [slides]
- Meeting of the Austrian Mathematical Society 2023 in Graz, Austria. Connecting Morse theory and persistent homology of geometric complexes. September 18, 2023.
- Computational Persistence 2022 workshop, online. Functorial nerve theorems for persistence. November 4, 2022. [slides] [recording]
- TGDA seminar at the OSU in Columbus, Ohio. Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations. September 27, 2022. [slides]
- NDAG seminar at the OSU in Columbus, Ohio. A Unified View on the Functorial Nerve Theorem and its Variations. September 8, 2022. [slides]
- Applied CATS seminar at the KTH in Stockholm, Sweden. A Unified View on the Functorial Nerve Theorem and its Variations. April 26, 2022. [slides]
Students advised
- Lewis Phu Ngo (2024, Semester Project, jointly with Ulrich Bauer): The Universal Coefficient Theorem for Homology: A Computational Approach
- Cristina Rothgiesser Balbuena (2023, Bachelor’s thesis, jointly with Ulrich Bauer): Shellability Is NP-Complete
- Sönke Clausen (2023, Master’s thesis, jointly with Ulrich Bauer): Robust and Efficient Computation of Cech Persistence Barcodes
- Markus Ruhland (2021, Bachelor’s thesis, jointly with Ulrich Bauer): Homological Algebra in Puppe-exact Categories
Teaching
- Topology (SS 23, Teaching Assistant)
- 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)