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, Hughes, Sam, Kielak, Dawid, and Mizerka, Piotr. “Non-vanishing unitary cohomology of low-rank integral special linear groups.” arXiv . doi: 10.48550/arXiv.2410.22310.
- Brück, Benjamin, Patzt, Peter, and Sroka, Robin J.. “A presentation of symplectic Steinberg modules and cohomology of Sp_2n(Z).” arXiv . doi: 10.48550/arXiv.2306.03180.
Research Articles (Journals)
- 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 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.
- Borinsky, Michael, Brück, Benjamin, and Willwacher, Thomas. “Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group.” Selecta Mathematica (New Series) doi: 10.48550/arXiv.2308.16845.
- 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.” arXiv . doi: 10.48550/arXiv.2404.15026.
- Brück, Benjamin, and Piterman, Kevin I.. “Connectivity of partial basis complexes of freely decomposable groups.” arXiv . doi: 10.48550/arXiv.2410.17121.
- Brück, Benjamin, Hughes, Sam, Kielak, Dawid, and Mizerka, Piotr. “Non-vanishing unitary cohomology of low-rank integral special linear groups.” arXiv . doi: 10.48550/arXiv.2410.22310.
- Brück, Benjamin, and Himes, Zachary. “Top-degree rational cohomology in the symplectic group of a number ring.” arXiv . doi: 10.48550/arXiv.2309.05456.
- Brück, Benjamin, Patzt, Peter, and Sroka, Robin J.. “A presentation of symplectic Steinberg modules and cohomology of Sp_2n(Z).” arXiv . doi: 10.48550/arXiv.2306.03180.
Research Articles (Journals)
- 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.
- 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, and Sroka, Robin J.. “Apartment classes of integral symplectic groups.” Journal of Topology and Analysis 2305.17697. 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) doi: 10.48550/arXiv.2308.16845.
- 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. “Between buildings and free factor complexes.” Dissertation thesis, Universität Bielefeld, .
Other Non-Scientific Publications
- 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. (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 \(\operatorname{SL}_n(\mathbb Z)\) 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.