Theses
Bachelor, Master and PhD
Past theses and suggested topics for future work. See also Math Genealogy Project.
Future topics
Literature and References
The papers listed below are foundational contributions to research in geometry and group theory. Each one offers a strong entry point into a vibrant topic of current research.
- J. Bourgain, On Lipschitz embedding of finite metric spaces in Hilbert space, Israel Journal of Mathematics 52 (1985), 46-52.
- D. Burago and B. Kleiner, Separated nets in Euclidean space and Jacobians of bi-Lipschitz maps, Geom. Funct. Anal. 8 (1998), 273-282.
- Y. de Cornulier and A. Mann, Some residually finite groups satisfying laws. Geometric group theory, 45–50, Trends Math., Birkhäuser, Basel, 2007.
- J. Howie, A proof of the Scott-Wiegold conjecture on free products of cyclic groups. J. Pure Appl. Algebra 173 (2002), no. 2, 167–176.
- W. Johnson and J. Lindenstrauss, Extensions of Lipschitz mappings into a Hilbert space, Contemp. Math. 26 (1984), 189-206.
- K. Whyte, Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture, Duke Math. J. 99 (1999), 93-112.
Completed theses
Doctoral theses
| Name | Year | Title | Institution |
|---|---|---|---|
| Lukas Gohla | 2024 | Topics in Group Stability | TU Dresden |
| Leonardo Businhani Biz | 2021 | The Boundary A-(T)-menability of the Space of Finite Bounded Degree Graphs (supervised by Vadim Alekseev) | TU Dresden |
| Jakob Schneider | 2020 | On ultraproducts of compact quasisimple groups | TU Dresden |
| Christiane Zyrus | 2020 | Almost laws for finite simple groups | TU Dresden |
| Maria Gerasimova | 2019 | Isoperimetry, Littlewood functions, and unitarisability of groups | TU Dresden |
| Anton Claußnitzer | 2018 | Aspects of p-adic operator algebras | TU Dresden |
| Marcus de Chiffre | 2018 | Approximate representations of groups | TU Dresden |
| Tom Drescher | 2018 | Free Convex Semi-Algebraic Geometry — The Limits of Quantifier Elimination, Projection Properties, and Operator Systems (supervised by Tim Netzer) | Universität Innsbruck |
| Abdelrhman Elkasapy | 2015 | Word Maps on Compact Lie Groups | Universität Leipzig |
| Andreas Kübel | 2015 | Equivariant Differential Cohomology | Universität Leipzig |
| Philip Dowerk | 2015 | Algebraic and Topological Properties of Unitary Groups of II1 factors | Universität Leipzig |
| Peter Schlicht | 2013 | Amenable groups and a geometric view on unitarisability | Universität Leipzig |
| Abel Stolz | 2013 | Linear approximation of groups and ultraproducts of compact simple groups | Universität Leipzig |
| Łukasz Grabowski | 2011 | On Turing machines, dynamical systems and the Atiyah problem | Georg-August-Universität Göttingen |
| Johannes Härtel | 2008 | Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen | Georg-August-Universität Göttingen |
Master's theses
| Name | Year | Title | Institution |
|---|---|---|---|
| Kenan Vrabac | 2025 | Amenability of finite energy path and loop groups | TU Dresden |
| Jakob Galley | 2024 | On the Jacobian Conjecture | TU Dresden |
| Max Schmidt | 2023 | Amenability for Unitary Groups of C*-Algebras | TU Dresden |
| Barbara Ueltzen | 2022 | On Knot Algebras and a Theorem of Kronheimer and Mrowka | TU Dresden |
| Philipp Mickan | 2021 | Equations in H-Spaces | TU Dresden |
| Frederic Dörband | 2019 | Solvability of Finite Groups | TU Dresden |
| Lukas Gohla | 2018 | On Margulis Normal Subgroup Theorem for Groups and Equivalence Relations (supervised by Vadim Alekseev) | TU Dresden |
| Jakob Schneider | 2016 | Laws for finite groups | TU Dresden |
| Christoph Gamm | 2011 | ε-representations of groups and Ulam stability | Georg-August-Universität Göttingen |
Bachelor's theses
| Name | Year | Title | Institution |
|---|---|---|---|
| Ron Ulitzsch | 2025 | Universelle Strukturen: Kategorientheorie mit Beispielen aus Linearer Algebra, Algebra und Algebraischer Geometrie (supervised by Julia Goedecke) | TU Dresden |
| Stefan Förster | 2025 | Gemischte Identitäten in projektiven speziellen linearen Gruppen der Dimension 2 (co-supervised with Jakob Schneider) | TU Dresden |
| Klemens Fritzsche | 2023 | Über die Weyl-Algebra | TU Dresden |
| Philipp Mickan | 2019 | Mittelbare Gruppen und der Satz von Bartholdi | TU Dresden |
| Tony Zorman | 2019 | From Knot Theory to Algebra | TU Dresden |
| Barbara Ueltzen | 2019 | On Khovanov’s cohomology as a link invariant | TU Dresden |
| Lorenz Breitsamter | 2019 | The Suzuki groups | TU Dresden |
| Theresa Schröter | 2019 | Die diophantische Eigenschaft von Elementen aus SO(3) | TU Dresden |
| Florian Starke | 2018 | Measure Concentration for Symplectic Groups | TU Dresden |
| Constantin Bilz | 2016 | Approximation of the Euclidean Plane by Metric Graphs | TU Dresden |
| Christoph Gamm | 2009 | ε-representations of amenable groups | Georg-August-Universität Göttingen |
| Patrick Neumann | 2009 | Durchmesser und Wachstum endlicher Heisenberggruppen | Georg-August-Universität Göttingen |
Staatsexamen für Lehramt
| Name | Year | Title | Institution |
|---|---|---|---|
| Fabian Schulz | 2018 | Das Vierfarbenproblem in außerschulischen Lernvorhaben | TU Dresden |
Diploma theses
| Name | Year | Title | Institution |
|---|---|---|---|
| Johannes Dietzschold | 2024 | The Fitting Lemma for Finite Tracial von Neumann Algebras | Universität Leipzig |
| Christian Fetsch | 2014 | Expandergraphen und Derandomisierung | Universität Leipzig |
| Christiane Zyrus | 2014 | Trace polynomials and word maps | Universität Leipzig |
| Tom Drescher | 2014 | Graphen und Determinantendarstellungen (supervised by PD Dr. Tim Netzer) | Universität Leipzig |
| Felix Weber | 2013 | Planarität und der Test auf Eigenschaften in dünnbesetzten Graphen | Universität Leipzig |
| Niklas Hase | 2013 | Entropy of algebraic actions | Universität Leipzig |
| Heinrich-Gregor Zirnstein | 2012 | Formulating Szemerédi's Theorem in Terms of Ultrafilters | Universität Leipzig |
| Andreas Kübel | 2011 | Die Stabile-Kohomotopie-Konstruktion von Bauer und Furuta (co-supervised with Matthias Schwarz) | Universität Leipzig |
| Daniel Rettstadt | 2009 | L2-Homology of Thompsons group | Georg-August-Universität Göttingen |
| Peter Schlicht | 2009 | L2-Homologie und die Vermutung von Whitehead | Georg-August-Universität Göttingen |