Research
Arithmetic groups
Arithmetic groups
Arithmetic groups such as SL_n(Z) combine number-theoretical, algebraic, and geometric aspects and appear in many mathematical contexts. We study them as lattices on symmetric spaces and Euclidean structures with respect to Kazhdan’s property (T) and Margulis’s normal subgroup property.
Finiteness Properties
Finiteness Properties
Topological finiteness properties generalize the properties of being finitely generated and finitely presented and are directly related to connectivity properties of spaces. We investigate finiteness properties of, among others, arithmetic groups, Thompson-like groups, and Kac–Moody groups.
Third-Party Funding
Our research is supported by the following third-party funded projects:
- Coarse Geometry of Simple Groups and Buildings, WI 4079/6, https://gepris.dfg.de/gepris/projekt/411567927, DFG Heisenberg Fellowship
- Geometric Invariants of Discrete and Locally Compact Groups, WI 4079/7, https://gepris.dfg.de/gepris/projekt/441648074, DFG research grant within the framework of Priority Programme 2026, https://spp2026.de/
- Finiteness Properties of Kac–Moody Groups, WI 4079/8, https://gepris.dfg.de/gepris/projekt/496757904, DFG research grant
- Fellowship for Dorian Chanfi funded by the Humboldt Foundation, https://www.humboldt-foundation.de/
Selected Publications
- Bux, K. U.; Köhl, R. und Witzel, S. 2013. Higher finiteness properties of reductive arithmetic groups in positive characteristic: The Rank Theorem. Annals of Mathematics 177: 311-366
- Skipper, R.; Witzel, S. und Zaremsky, M. C. B. 2019. Simple groups separated by finiteness properties. Inventiones mathematicae 215: 713-740
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Witzel, S. 2014. Finiteness Properties of Arithmetic Groups Acting on Twin Buildings. Springer Cham Heidelberg New York Dordrecht London