Which topics do I offer?

My research interests are quite diverse, so that I may accommodate many different directions for bachelor's and master's theses. This includes, among others:

Algebraic Topology
some parts of C*-Algebras and K-Theory
some parts of Differential and Riemannian Geometry
some parts of Functional Analysis, especially involving applications to mathematical physics
Homological Algebra
(geometric) group theory
groupoids.

The list of previous bachelor's and master's theses listed below give you more concrete ideas of possible topics. I have a somewhat messy file with ideas for thesis projects (collected over the course of many years and not tidied up often enough). If you are interested in a project, an individual meeting with a discussion of the options must and will be scheduled (every person is different, with different interests and strengths and background, also my interests are always shifting).

Zwei-Fächer-Bachelor und Master of Education?

Ich habe bisher acht Bachelorarbeiten im 2-FBA und 3 Staatsexamensarbeiten betreut, und betreue aktuell eine Masterarbeit im Master of Education. Ich bin mir bewusst, dass Studierende in diesen Studiengängen nur wenige Mathematikvorlesungen belegen können, so dass wir Themen wählen, die weniger voraussetzen (je nach den individuellen Kenntnisse). Die Gebiete waren in der Vergangenheit breit gestreut, siehe die Liste unten.

When and how best to contact me?

Please stop by or send me an email to ask for an appointment. It is useful for me if you write also about the kind of mathematics that you particularly like and/or some of the subjects that you have already learnt or are learning right now, especially those that you enjoy doing and would like to figure in your thesis project. If you approach me well in advance, there would be some time for you to take courses suitable to prepare you for a thesis topic in a particular direction. That is why I recommend to approach me early if you are interested in a thesis with me. If you come to a week before you want to start working on your thesis, it may work out nicely or it might not.

Note that there are many professors in Göttingen which do interesting mathematics. I recommend to talk to several before making a commitment for a particular thesis project.

Previous and current Bachelor Projects

(2023): Spectral theory and algebras of unbounded operators. Finite regularized dimension.
(2023): The Jones index theorem and aspects of the theory of Temperlie-Lieb algebras.
(2023): The Mayer-Vietoris sequence in coarse homology
(2023): Topological insulators and computations of mapping spaces.
(2023): Geometry and topology of (Riemannian) surfaces using concrete examples
(2023): Topological complexity of atoroidal symplectic spaces
(2023): A homological proof of Bott periodicity
(2023): Cohomology of orbifolds via differentiable stacks
(2023): The Bochner technique in complex geometry
(2023): Spacetime harmonic functions and the positive mass theorem (also with boundary)
(2023): The construction of higher groups from crossed modules and crossed complexes
(2022): Homotopy theory of model categories in algebra and geometry
(2022): Topologische Komplexität von Gruppen
(2022): Klassifikation muliplektischer Strukturen in speziellen Fällen
(2022): Homologische Algebra und Gruppenkohomologie
(2022): Spectral sequences and applications
(2021): Bundle theory and Postnikov towers
(2020): A loop space bundle model of T-duality
(2020): Doppelschichtpotentiale zur Lösung der Laplace-Gleichung
(2020): The Wall finiteness conditions and geometric consequences
(2020). Morse theory: Beweis von reeller Bott Periodizität
(2020) Theorie und Anwendung der Laplace-Transformation bei DGls und möglicher Schulbezug
(2019): Morse Theory of moment maps

Previous and current Master thesis projects

(2022): Constructions of isospectral surfaces
(2023): Homological stability for bounded cohomology of unitary groups
(2023): Geometric twisting of MU-Bordismus via $KO^1$ as "Lift" of twists of K-theory by HZ2
(2024): A-Dachgeschlecht und getwistete K-Theorie/Azumaya-Algebren

Frühere und aktuelle Projekte 2-Fächer BA (Lehramt)

(2022): Wachstum kristallographischer Strukturen
(2020): Field of formal Laurent-Series, specific Subrings and their Application in Proofs of Transcendence
(2020): Writhing und linking number
profinite groupos and Galois-Theorie
(2019): Divergente Reihen in der Mathematik
(2019): Eigenwerttheorie Sturmscher Randwertprobleme

Frühere und aktuelle Projekte Master of Education

(2023) (ME): Potenzreihenringe und -körper in mehreren Variablen