Research
Table of Contents
My research mainly focuses on topological and combinatorial properties of geometric complexes as well as their use in topological data analysis. Recently, I have also become interested in machine learning in general, especially large language models.
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] [bioRxiv] [git]
- A unified view on the functorial nerve theorem and its variations – with Ulrich Bauer, Michael Kerber, Alexander Rolle. Expositiones Mathematicae. [doi] [arxiv] [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]
- 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)