On this page, you can learn about the research and teaching I was involved in during my time as a PhD student (until September 2025).
Research
An explanation of my research to non-mathematicians can be found here.
PhD Thesis
Bounding torsion homology growth: algebraic cheap rebuilding, inner amenability and dynamics (pdf)
supervised by Prof. Dr. Clara Löh
The DOI is 10.5283/epub.77926.
(Pre)prints
The cheap embedding principle: Dynamical upper bounds for homology growth (pdf)
joint work with Kevin Li, Clara Löh, Marco Moraschini and Roman Sauer
arXiv: 2508.01347 [math.AT]
Algorithms in 4-manifold topology (pdf)
joint work with Stefan Bastl, Rhuaidi Burke, Rima Chatterjee, Subhankar Dey, Alison Durst, Stefan Friedl, Daniel Galvin, Alejandro García Rivas, Tobias Hirsch, Cara Hobohm, Chun-Sheng Hsueh, Marc Kegel, Frieda Kern, Shun Ming Samuel Lee, Clara Löh, Naageswaran Manikandan, Léo Mousseau, Lars Munser, Mark Pencovitch, Patrick Perras, Mark Powell, José Pedro Quintanilha, Lisa Schambeck, David Suchodoll, Martin Tancer, Annika Thiele, Paula Truöl, Simona Veselá, Melvin Weiß, and Magdalina von Wunsch-Rolshoven
arXiv: 2411.08775 [math.GT]
To appear in Algebraic and Geometric Topology
The algebraic cheap rebuilding property (pdf)
joint work with Kevin Li, Clara Löh, Marco Moraschini and Roman Sauer
arXiv: 2409.05774 [math.GR]
To appear in Transactions of the AMS
Torsion homology growth and cheap rebuilding of inner-amenable groups (pdf)
arXiv: 2212.07916 [math.GR]
Original Publication in Groups, Geometry and Dynamics, vol. 19, no. 3, pp. 1089–1105, 2025. The DOI is 10.4171/GGD/803.
\(L^2\)-Betti numbers and computability of reals (pdf)
joint work with Clara Löh
(Partial) Implementation in Lean
arXiv: 2202.03159 [math.GR]
Original Publication in Computability, vol. 12, no. 2, pp. 175-201, 2023. The DOI is 10.3233/COM-220416.
Lean
Amenable Groups in Lean, September 2022 (repository)
Master Thesis
Computability and \(\ell^2\)-Betti Numbers (pdf)
The DOI is 10.5283/epub.51433
(Partial) Implementation in Lean
Invited Talks
I was invited to give the following talks.
| 18.06.2025 | "A dynamical upper bound on logarithmic torsion homology growth" | Online Seminar on Probabilistic and Geometric Group Theory | Online |
| 16.04.2025 | "A dynamical upper bound on logarithmic torsion homology growth" | Manifolds and groups in Bologna, III | Università di Bologna |
| 11.11.2024 | "Computability in Topology: Mapping degree sets between manifolds" | Oberseminar Mathematische Logik | Universität Würzburg |
| 27.06.2024 | "Mapping degree sets between manifolds" | Geometry + Groups Seminar | Universität Heidelberg |
| 28.05.2024 | "Insiemi di gradi topologici tra varietà (Mapping degree sets between manifolds)" | Seminari dei Baby Geometri | SNS Pisa |
| 02.05.2024 | "A dynamical criterion for vanishing homology growth" | AG-Seminar Topologie und Geometrische Gruppentheorie | KIT Karlsruhe |
| 11.04.2024 | Poster presentation "Inner-amenable groups and homology growth" (Poster) | Young Geometric Group Theory XII | University of Bristol |
| 21.03.2024 | "Torsion homology growth and cheap rebuilding of inner-amenable groups" | Topological and Homological Methods in Group Theory | University of Bielefeld |
| 24.11.2023 | "Homology growth and cheap rebuilding of inner-amenable groups" | Groups, Dynamics and Topology Seminar | Jagiellonian University, Cracow |
| 10.10.2023 | "From Amenable to Inner-Amenable" (Gong Talk Slides) | Autumn School on Large Scale Geometry | Universität Göttingen |
| 26.09.2023 | "Amenable Groups in Lean" (Slides) | Summer school Interactions of Proof Assistants and Mathematics | Universität Regensburg |
| 11.09.2023 | "From Amenable to Inner-Amenable" (Gong Talk Slides) | GRAZP 2023 | Ventotene |
| 06.12.2022 | "Homology growth of inner amenable groups in degree one" | Oberseminar Topology | Universität Göttingen |
| 27.09.2022 | "Implementing Amenable Groups in Lean" (Source code) | Workshop Recent Advances in Bounded Cohomology | University of Regensburg |
| 09.05.2022 | "\(L^2\)-Betti numbers and computability of reals" | International young seminar on bounded cohomology and simplicial volume | Online |
| 24.03.2022 | "Computability of \(L^2\)-Betti Numbers" | Geometry Graduate Colloquium | ETH Zürich |
| 21.01.2022 | "Computability and \(\ell^2\)-Betti Numbers" | Oberseminar Algebra und Geometrie | Heinrich Heine-Universität Düsseldorf |
Teaching
As a student, and later as a PhD student, I was involved in teaching of the following courses.
Summer term 2025
- Coorganiser of the Regensburg GAP days (joint with Eleni Hübner-Rosenau, Chiara Sabadin, and Malena Wasmeier)
- Lecturer of Examenskurs Algebra und Zahlentheorie (Lehramt Gymnasium) (joint with Florian Strunk)
Winter term 2024/25
- TA for Graphs, Groups, Topology and Computational Complexity
- Organiser of the Online Seminar on Bounded Cohomology and Simplicial Volume (joint with Giuseppe Bargagnati and Kevin Li)
Summer term 2024
- Tutor for Algebraic Topology III.5
- Organiser of the HIOB Gromov-Hausdorff convergence and metric geometry (joint with Jonathan Glöckle and Julian Seipel)
- Organiser of the Online Seminar on Bounded Cohomology and Simplicial Volume (joint with Federica Bertolotti and Kevin Li)
- Organiser of a workshop on profinite rigidity at KIT Karlsruhe (joint with Benjamin Brück, Jerónimo García-Mejía and Kevin Klinge)
Winter term 2023/24
- TA for Decision problems in groups
- TA for Grundlagen der Mathematik/Lineare Algebra I (FIDS)
- Organiser of the Online Seminar on Bounded Cohomology and Simplicial Volume (joint with Federica Bertolotti and Kevin Li)
Summer term 2023
- TA for CAT(0)-cube complexes
- TA for Geometrie für Lehramt Gymnasium
- Organiser of the Online Seminar on Bounded Cohomology and Simplicial Volume (joint with Federica Bertolotti and Kevin Li)
- Tutor for Schnupperstudium Mathematik
Winter term 2022/23
- TA for Open Covers and complexity (à la Lusternik–Schnirelmann)
- Tutor for Applied Algebraic Topology
- Organiser of the Online Seminar on Bounded Cohomology and Simplicial Volume (joint with Federica Bertolotti and Kevin Li)
Summer term 2022
- Tutor for Geometric Group Theory
Winter term 2021/22
- TA for Proof Lab: Simplicial Topology
- Tutor for Algebraic Topology
Summer term 2021
- Tutor for Geometrie (Lehramt Gymnasium)
Winter term 2020/21
- Tutor for Analysis I
Summer term 2020
- Tutor for Analysis auf Mannigfaltigkeiten (Analysis IV)
Summer term 2019
- Tutor for Einführung in Wahrscheinlichkeitstheorie und Statistik
Winter term 2018/19
- Tutor for Algebra
Summer term 2018
- Tutor for Lineare Algebra II
Winter term 2017/18
- Tutor for Lineare Algebra I