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
- Habilitation in mathematics, University of Münster
- 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)
Projects
- EXC 2044 - T01: K-Groups and cohomology ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/2, T1 - EXC 2044 - T03: Models and universes ()
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/2, T3 - High-dimensional cohomology of arithmetic groups ()
Individual Granted Project: DFG - Individual Grants Programme | Project Number: BR 7190/2-1
- EXC 2044 - T01: K-Groups and cohomology ()
Publications
Selection
Research Articles in a Digital Collection
- 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, Hughes, Sam, Kielak, Dawid, and Mizerka, Piotr. . “Non-vanishing unitary cohomology of low-rank integral special linear groups.” International Mathematics Research Notices 2025 (15). doi: 10.1093/imrn/rnaf230.
- 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, 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, 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, Hughes, Sam, Kielak, Dawid, and Mizerka, Piotr. . “Non-vanishing unitary cohomology of low-rank integral special linear groups.” International Mathematics Research Notices 2025 (15). doi: 10.1093/imrn/rnaf230.
- 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, and Piterman, Kevin I. in Kürze. “Connectivity of partial basis complexes of freely decomposable groups.” Preprint. Bulletin of the London Mathematical Society 2410.17121. doi: 10.48550/arXiv.2410.17121.
- 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, Harnois-Déraps, Joachim, Unruh, Sandra, Castro, Tiago, Dolag, Klaus, and Martinet, Nicolas. . “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. . “(Non-)Vanishing of high-dimensional group cohomology.” Habilitation thesis, Universität Münster.
- Brück, Benjamin. . “Between buildings and free factor complexes.” Dissertation thesis, Universität Bielefeld.
Other Non-Scientific Publication
- Hunger, Uwe (Hrsg.), Krannich, Sascha (Hrsg.), Brück, Benjamin, Guilliard, Simon, Jaculi, Linda, Krekel, Julia, Mieger, Hannah, Neumann, Insa, Pham, YLan, Polovnikov, Borislav, Pretzsch, Rebecca, Rollfing, Petra, Schüler, Theresa, Stumptner, Quincey, Wagner, Julia, Wollweber, Benjamin, and Sadjadi, Mahan. . Wissenschaftliche Schriften der WWU Münster, Vol. VII, Über Brücken und Grenzen entlang der Donau, edited by M Sadjadi. readbox unipress.
PD 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 \(\operatorname{SL}_n(\mathbb Z)\) using Voronoi tesselations, see SLnCohomology.
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.