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Projects/Supervision
- Interested in working on a project under my supervision? Just send me an email or come to my office hours!
- Further supervisors and topics in the Global Analysis group can be found here.
Types of projects
I am happy to supervise the following types of projects:-
Bachelorarbeiten (BSc Mathematik, BSc Computational Science)
- expository work
- mini research project
- algorithmic aspects and implementation
-
Zulassungsarbeiten (Lehramt vertieft/Gymnasium)
- expository work
- outreach/popularisation (e.g., high school students, but also non-mathematical audience)
- mini research project
- algorithmic aspects and implementation
- real world applications of theoretical mathematics
-
Masterarbeiten (MSc Mathematik)
- expository work
- small research project
- algorithmic aspects and implementation
- PhD projects in geometric topology, geometric group theory, measurable group theory.
Some general advice on writing/presenting mathematics
- Slippery Slides GK-Ringvorlesung, January 2018.
- Exercises in Academic Writing GK-Ringvorlesung, May 2017.
- Allgemeines zum mathematischen Schreiben (in German)
- Save early, save often! (most of this applies also to popular version control systems such as git or Mercurial)
Topics
Possible fields for projects under my supervision include the following:- geometric topology
- algebraic topology of manifolds
- geometric group theory
- measured group theory
- combinatorial group theory
- group cohomology
- graph theory (in particular, infinite graphs)
- algorithmic topology
- operator algebras in algebraic/geometric topology
- metric geometry
- formalisation of mathematics in proof assistants
| Topic | Type | Prerequisites |
| Games with projective geometry; | Zula; | geometry |
| Error-correcting codes; | Zula, Bsc (Math, Comp Science); | algebra |
| Linear feedback shift registers; | Zula, Bsc (Math, Comp Science); | algebra |
| Classifying spaces of one-relator groups; | BSc (Math); | algebraic topology |
| Fuglede--Kadison determinants | BSc (Math); | functional analysis |
| Uniqueness of Slitherlink curves; | Zula, BSc (Math, Comp Science); | basic math courses (plus some geometry) |
| Accessibility proofs in computer games; | Zula, BSc (Math, Comp Science), MSc (Comp Science); | programming skills, mathematical logic |
| Verification of theorems in proof assistants; | any; | programming skills, mathematical logic |
| Simplicial volume with twisted coefficients; | MSc (Math); | algebraic and geometric topology |
| Non-verbal mathematics; | Zula, BSc (Math); | basic math courses |
| 3D optical illusions; | Zula, BSc (Comp Science) | basic math courses |
| Computational complexity of classical games; | Zula, Bsc (Math, Comp Science); | basic math courses |
| Model-theoretic aspects of geometric group theory; | BSc (Math), MSc (Math); | geometric group theory, mathematical logic |
| Categories for measure equivalence of groups; | BSc (Math), MSc (Math); | basic math courses |
| Comparison of homological gradient invariants; | BSc (Math), MSc (Math); | algebraic topology |
| Profinite rigidity; | BSc (Math), MSc (Math) | algebraic topology/group homology or geometric group theory |
| Inner amenability; | BSc (Math), MSc (Math); | group theory, functional analysis |
| The equivalence theorem for relative simplicial volume, explicitly; | MSc (Math); | algebraic and geometric topology |
| Ergodic theoretic methods in simplicial volume; | MSc (Math) | algebraic/geometric topology, group homology, functional analysis |
| Computability of values of numerical topological invariants; | MSc (Math) | algebraic/geometric topology, mathematical logic |
| The amenable reduction lemma; | MSc (Math) | algebraic/geometric topology or geometric group theory |
Supervised projects
- Gleichmäßig endliche Homologie im Grad 0 (Bachelor Mathematics, 2025)
- Parametrized automata over infinite alphabets: Propertie and complementation (Master Computational Science, 2024; lead supervisor: Philipp Rümmer)
- Combinatorial topology: cubes and simplices (Master Mathematics, 2024)
- Profinite rigidity and amenability (Master Mathematics, 2024)
- G-Theory of group rings (Master Mathematics, 2024)
- Hyperbolic reflection groups (Zulassungsarbeit zum Staatsexamen Mathematics, 2024)
- Large homology spheres (Master Mathematics, 2024)
- Wachstumsfunktionen und Wachstumsreihen endlich erzeugter Gruppen (Zulassungsarbeit zum Staatsexamen Mathematics, 2024)
- Hyperbolisches Volumen und exponentielle Wachstumsraten (Master Mathematics, 2023)
- Minimal volume entropy of simplicial complexes (Master Mathematics, 2023)
- Minimal volume estimates and nerves of open covers (Master Mathematics, 2023)
- Persistent homology analysis of the evolution of SARS-CoV-2 (Bachelor Mathematics, 2023)
- Acyclic groups (Master Mathematics, 2023)
- Irrational simplicial volumes (Master Mathematics, 2023)
- Quasi-morphisms and bounded cohomology (Master Mathematics, 2023)
- Geometric von Neumann problems on non-amenability (Master Mathematics, 2023)
- Counterexamples to Kaplansky's unit conjecture (Master Mathematics, 2023)
- A Monster's Expedition (through Puzzling Exhibitions) -- eine mathematische Analyse (Zulassungsarbeit zum Staatsexamen Mathematics, 2023)
- Universality and examples in the context of functorial semi-norms (Johannes Witzig, Dr. rer. nat., 2023)
- Expander graphs -- old and new methods (Master Mathematics, 2023, co-superviison with Prof. P. Stellari, Milano)
- Eine Quasiisometrie-invariante Gendarm-Zahl (Bachelor Mathematics, 2023)
- Homologiesphären (Bachelor Mathematics, 2023)
- A formalisation of the Švarc-Milnor lemma in Lean (summer project, 2022)
- Integral foliated simplicial volume and ergodic decomposition (Master Mathematics, 2022)
- Applications of Topological Data Analysis to Functional Brain Analysis (Master Mathematics, 2022)
- Three slices of 3-manifold topology: spatial graphs, surface complexes and simplicial volumes (José Pedro Quintanilha, Dr. rer. nat., 2022; co-supervision with Prof. Dr. S. Friedl)
- Surjunctive groups (Bachelor Mathematics, 2021)
- Spectral sequences in bounded cohomology (Master Mathematics, 2021)
- Simplicial volume and non-positive curvature (Master Mathematics, 2021)
- Computability and L2-Betti numbers (Master Mathematics, 2021)
- CAT(0)-Spaces and the Cartan fixed point theorem (Bachelor Mathematics, 2021)
- Homology with S-module coefficients in the Isabelle proof assistant (Master Mathematics, 2020)
- Real-world amenable coverage problems and bounded cohomology (Master Mathematics, 2020)
- Integral foliated simplicial volume of mapping tori (Master Mathematics, 2020)
- The Hopf conjecture for self-maps (Master Mathematics, 2020)
- Hyperbolic one-relator groups (Master Mathematics, 2020)
- Die Eigenschaft UBC auf freien Gruppen (Bachelor Mathematics, 2019)
- Homologische Algebra für l^1-Homologie (Bachelor Mathematics, 2019)
- Die l^1-Halbnorm auf singulärer Homologie im Grad 2 (Bachelor Mathematics, 2019)
- Hashing via Expandergraphen (Bachelor Mathematics, 2019)
- Das Svarc-Milnor Lemma und 4-Mannigfaltigkeiten (Bachelor Mathematics/Zulassungsarbeit zum Staatsexamen Mathematics, 2019)
- Deskriptive Mengenlehre und Forcing (Bachelor Mathematics, 2019)
- Classifying spaces and orbit categories (Bachelor Mathematics, 2019)
- Parametrised simplicial volume and S^1-actions (Daniel Fauser, Dr. rer. nat., 2019)
- Chromatic number of groups (Bachelor Mathematics, 2019)
- Hochschild and cyclic homology for bornological coarse spaces (Luigi Caputi, Dr. rer. nat., 2019; primary supervisor: Prof. Dr. U. Bunke)
- Epimorphism testing for virtually Abelian groups (Master Computational Science, 2019)
- Hopfalgebren in der Galoistheorie (Bachelor Mathematics, 2018)
- Machine learning solutions of combination puzzles (Bachelor Mathematics, 2018)
- Hilbert spaces over non-archimedean fields (Bachelor Mathematics, 2018)
- Simplicial volume of surfaces with finite coefficients (Bachelor Mathematics, 2018)
- Formalisation of the topology of surfaces (DAAD-WISE, 2018)
- Formalisation of quasi-geometry (DAAD-WISE, 2018)
- Counting triangulated manifolds (Master Mathematics, 2017)
- Präkategorien und Phylogenetik (Bachelor Mathematics, 2017)
- Hyperbolicity and linear isoperimetric inequalities (Bachelor Mathematics, 2016)
- Groups with context-free normal form (Master Mathematics, 2016)
- Verified aspherical universal realisation of cycles (Master Mathematics, 2016)
- Secondary simplicial volume of 3-manifolds (Master Mathematics, 2016)
- Fasererhaltende Quasi-Isometrien (Bachelor Mathematics, 2015)
- Mannigfaltigkeiten mit niedrigem ganzzahligem simplizialem Volumen (Master Mathematics, 2015)
- Cayley graphs of free groups: a probabilistic and a geometric approach (Master Mathematics, 2015)
- Kubisches simpliziales Volumen (Master Mathematics, 2015)
- Relative bounded cohomology for groupoids (Matthias Blank, Dr. rer. nat., 2015)
- Aspects of uniformly finite homology (Francesca Diana, Dr. rer. nat., 2014)
- Kubisches simpliziales Volumen von Flächen (Bachelor Mathematics, 2014)
- Classification of Loop Agreement Tasks (Bachelor Computational Science, 2014)
- Abzählbare geometrische Träger für l1-Homologieklassen (Bachelor Mathematics, 2014)
- Endliche funktorielle Halbnormen und Darstellbarkeit (Bachelor Mathematics, 2013)
- Triangulierungen von Mannigfaltigkeiten (Bachelor Mathematics, 2013)
- Der Satz von Hales-Jewett (Zulassungsarbeit zum Staatsexamen, Mathematics, 2013)
- Noethersche Gruppenringe (Zulassungsarbeit zum Staatsexamen, Mathematics, 2013)
- Aperiodische Täfelungen und gleichmäßig endliche Homologie (Diplom Mathematics, 2012)
- Gilmans Charakterisierung hyperbolischer Grupppen durch kontextfreie Sprachen (Diplom Mathematics, 2012)
- Wachstumsfunktionen endlich erzeugter abelscher Gruppen (Diplom Mathematics, 2012)
- Torsionsfreie Gruppen ohne "eindeutige Produkte" (Zulassungsarbeit zum Staatsexamen, Mathematics, 2012)
- Ultraprodukte und Ultralimiten in der Geometrischen Gruppentheorie (Bachelor Mathematics, 2012)
- Kategorien für Quasi-Geometrie (Bachelor Mathematics, 2012)
- Thompsons Gruppe F und ihre graphischen Darstellungen (Bachelor Mathematics, 2012)
- Kanten- und Knotenperkolation (Bachelor Mathematics, 2011)
- Die Wachstumsrate nilpotenter Gruppen (Bachelor Mathematics, 2011)
- Ramsey-Zahlen und Färbungsspiele auf Graphen (Zulassungsarbeit zum Staatsexamen, Mathematics, 2011)
- Die spieltheoretische chromatische Zahl (Zulassungsarbeit zum Staatsexamen, Mathematics, 2011)
