Research Focus
Geometric group theory
Groups, which are algebraic structures used for describing symmetries, play a central role in my work. The tools I use for studying these often involve topology, but also include methods from combinatorics, probability theory and logic.
CV
Academic Education
- PhD in mathematics, Bielefeld University
- Master in mathematics, University of Münster
- Bachelor in mathematics, University of Münster
Positions
- Akademischer Rat auf Zeit (advanced postdoc position), University of Münster
- Wissenschaftlicher Mitarbeiter (Postdoc), University of Münster
- Hermann-Weyl-Instructor, ETH Zürich
- Postdoctoral researcher, University of Copenhagen
External Function
- Mathematics Münster (Young Research Group - "High-dimensional cohomology of arithmetic groups", Investigator)
Publications
Selection
Research Articles in Digital Collections
- Brück, Benjamin, Patzt, Peter, and Sroka, Robin J. . “A presentation of symplectic Steinberg modules and cohomology of Sp_2n(Z).” Preprint. arXiv doi: 10.48550/arXiv.2306.03180.
Research Articles (Journals)
- Borinsky, Michael, Brück, Benjamin, and Willwacher, Thomas. . “Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group.” Selecta Mathematica (New Series), № 31 22. doi: 10.1007/s00029-025-01018-9.
- Brück, Benjamin, and Himes, Zachary. . “Top-degree rational cohomology in the symplectic group of a number ring.” Selecta Mathematica (New Series), № 31 55. doi: 10.1007/s00029-025-01051-8.
- Brück, Benjamin, Miller, Jeremy, Patzt, Peter, Sroka, Robin J., and Wilson, Jennifer C. H. . “On the codimension-two cohomology of SL_n(Z).” Advances in Mathematics, № 451 doi: 10.1016/j.aim.2024.109795.
- Brück, Benjamin, Piterman, Kevin I., and Welker, Volkmar. . “The common basis complex and the partial decomposition poset.” International Mathematics Research Notices, № 2024 (18): 12746–12760. doi: 10.1093/imrn/rnae177.
- Brück, Benjamin, Hughes, Sam, Kielak, Dawid, and Mizerka, Piotr. in Kürze. “Non-vanishing unitary cohomology of low-rank integral special linear groups.” Preprint. International Mathematics Research Notices doi: 10.48550/arXiv.2410.22310.
- Brück, Benjamin, and Garin, Adélie. . “Stratifying the space of barcodes using Coxeter complexes.” Journal of Applied and Computational Topology, № 7: 369–395. doi: 10.1007/s41468-022-00104-7.
- Brück, Benjamin. . “Between buildings and free factor complexes: A Cohen–Macaulay complex for Out(RAAGs).” Journal of the London Mathematical Society, № 105 (1): 251–307. doi: 10.1112/jlms.12511.
- Heydenreich, Sven, Brück, Benjamin, and Harnois-Déraps, Joachim. . “Persistent homology in cosmic shear: Constraining parameters with topological data analysis.” Astronomy and Astrophysics, № 648: A74. doi: 10.1051/0004-6361/202039048.
- Brück, Benjamin, and Gupta, Radhika. . “Homotopy type of the complex of free factors of a free group.” Proceedings of the London Mathematical Society, № 121 (6): 1737–1765. doi: 10.1112/plms.12381.
Complete List
Research Articles in Digital Collections
- Brück, Benjamin. . “(Non-)Vanishing of high-dimensional group cohomology.” Preprint. arXiv doi: 10.48550/arXiv.2404.15026.
- Brück, Benjamin, and Piterman, Kevin I. . “Connectivity of partial basis complexes of freely decomposable groups.” Preprint. arXiv doi: 10.48550/arXiv.2410.17121.
- Brück, Benjamin, Patzt, Peter, and Sroka, Robin J. . “A presentation of symplectic Steinberg modules and cohomology of Sp_2n(Z).” Preprint. arXiv doi: 10.48550/arXiv.2306.03180.
Research Articles (Journals)
- Brück, Benjamin, and Sroka, Robin J. . “Apartment classes of integral symplectic groups.” Journal of Topology and Analysis, № 17 (06): 1821–1840. doi: 10.1142/S1793525324500286.
- Borinsky, Michael, Brück, Benjamin, and Willwacher, Thomas. . “Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group.” Selecta Mathematica (New Series), № 31 22. doi: 10.1007/s00029-025-01018-9.
- Brück, Benjamin, and Himes, Zachary. . “Top-degree rational cohomology in the symplectic group of a number ring.” Selecta Mathematica (New Series), № 31 55. doi: 10.1007/s00029-025-01051-8.
- Brück, Benjamin, Fournier-Facio, Francesco, and Loeh, Clara. . “Median quasimorphisms on CAT(0) cube complexes and their cup products.” Geometriae Dedicata, № 218 28. doi: 10.1007/s10711-023-00870-3.
- Brück, Benjamin, Miller, Jeremy, Patzt, Peter, Sroka, Robin J., and Wilson, Jennifer C. H. . “On the codimension-two cohomology of SL_n(Z).” Advances in Mathematics, № 451 doi: 10.1016/j.aim.2024.109795.
- Brück, Benjamin, Santos Rego, Yuri, and Sroka, Robin J. . “On the top-dimensional cohomology of arithmetic Chevalley groups.” Proceedings of the American Mathematical Society, № 152 (10): 4131–4139. doi: 10.1090/proc/16948.
- Brück, Benjamin, Piterman, Kevin I., and Welker, Volkmar. . “The common basis complex and the partial decomposition poset.” International Mathematics Research Notices, № 2024 (18): 12746–12760. doi: 10.1093/imrn/rnae177.
- Brück, Benjamin, Hughes, Sam, Kielak, Dawid, and Mizerka, Piotr. in Kürze. “Non-vanishing unitary cohomology of low-rank integral special linear groups.” Preprint. International Mathematics Research Notices doi: 10.48550/arXiv.2410.22310.
- Wade, Richard D., and Brück, Benjamin. . “A note on virtual duality and automorphism groups of right-angled Artin groups.” Glasgow Mathematical Journal, № 65 (3): 573 –581. doi: 10.1017/s0017089523000149.
- Brück, Benjamin, and Garin, Adélie. . “Stratifying the space of barcodes using Coxeter complexes.” Journal of Applied and Computational Topology, № 7: 369–395. doi: 10.1007/s41468-022-00104-7.
- Brück, Benjamin. . “Between buildings and free factor complexes: A Cohen–Macaulay complex for Out(RAAGs).” Journal of the London Mathematical Society, № 105 (1): 251–307. doi: 10.1112/jlms.12511.
- Brück, Benjamin, and Röttger, Frank. . “A Central Limit Theorem for the Two-Sided Descent Statistic on Coxeter Groups.” Electronic Journal of Combinatorics, № 29 (1) P1.1. doi: 10.37236/10744.
- Heydenreich, Sven, Brück, Benjamin, Burger, Pierre, et al. . “Persistent homology in cosmic shear II. A tomographic analysis of DES-Y1.” Astronomy and Astrophysics, № 667: A125. doi: 10.1051/0004-6361/202243868.
- Heydenreich, Sven, Brück, Benjamin, and Harnois-Déraps, Joachim. . “Persistent homology in cosmic shear: Constraining parameters with topological data analysis.” Astronomy and Astrophysics, № 648: A74. doi: 10.1051/0004-6361/202039048.
- Brück, Benjamin, Kielak, Dawid, and Wu, Xiaolei. . “The Farrell–Jones conjecture for normally poly-free groups.” Proceedings of the American Mathematical Society, № 149: 2349–2356. doi: 10.1090/proc/15357.
- Brück, Benjamin. . “Higher generating subgroups and Cohen–Macaulay complexes.” Proceedings of the Edinburgh Mathematical Society, № 63 (1): 275–285. doi: 10.1017/S0013091519000415.
- Brück, Benjamin, and Gupta, Radhika. . “Homotopy type of the complex of free factors of a free group.” Proceedings of the London Mathematical Society, № 121 (6): 1737–1765. doi: 10.1112/plms.12381.
- Brück, Benjamin. . “Maximal hyperbolic towers and weight in the theory of free groups.” Mathematical Proceedings, № 170 (3): 479–498. doi: 10.1017/S0305004119000483.
Theses (Doctoral or Postdoctoral)
- Brück, Benjamin. . “Between buildings and free factor complexes.” Dissertation thesis, Universität Bielefeld.
Other Non-Scientific Publications
- Hunger, Uwe (Hrsg.), Krannich, Sascha (Hrsg.), Brück, Benjamin, et al. . Wissenschaftliche Schriften der WWU Münster, Vol. VII, Über Brücken und Grenzen entlang der Donau, edited by M Sadjadi. Dortmund: readbox unipress.
Dr. Benjamin Brück
Code
In addition to my publications above, my Github Page contains publicly available code that I used in research projects.
For the article Non-vanishing unitary cohomology of low-rank integral special linear groups with S. Hughes, D. Kielak and P. Mizerka, we wrote Julia code for computing cohomology of SLn(Z) using Voronoi tesselations, see SLnCohomology.
Open PhD position
I recently got a grant by the DFG (German Research Foundation) that allows me to fund a Doctoral student. The project will be related to the cohomology of Chevalley groups. The position will be advertised towards the end of 2025 for a start in 2026. Contact me if you would like to have further details.
Young Research Group
Robin J. Sroka and I form the Young Research Group "High-dimensional cohomology of arithmetic groups" at the Cluster of Excellence Mathematics Münster.