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
Research Articles in Digital Collections
- . (Non-)Vanishing of high-dimensional group cohomology. arXiv, . doi: 10.48550/arXiv.2404.15026. [submitted / under review]
- Connectivity of partial basis complexes of freely decomposable groups. arXiv, . doi: 10.48550/arXiv.2410.17121. [submitted / under review]
- . Non-vanishing unitary cohomology of low-rank integral special linear groups. arXiv, . doi: 10.48550/arXiv.2410.22310. [submitted / under review]
- . Top-degree rational cohomology in the symplectic group of a number ring. arXiv, . doi: 10.48550/arXiv.2309.05456. [submitted / under review]
- . Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group. arXiv, . doi: 10.48550/arXiv.2308.16845. [submitted / under review]
- A presentation of symplectic Steinberg modules and cohomology of Sp_2n(Z). arXiv, . doi: 10.48550/arXiv.2306.03180. [submitted / under review]
Research Articles (Journals)
- .“Median quasimorphisms on CAT(0) cube complexes and their cup products.” Geometriae Dedicata 218 (): 28. doi: 10.1007/s10711-023-00870-3.
- “On the codimension-two cohomology of SL_n(Z).” Advances in Mathematics 451 (). doi: 10.1016/j.aim.2024.109795.
- “On the top-dimensional cohomology of arithmetic Chevalley groups.” Proceedings of the American Mathematical Society 152, № 10 (): 4131–4139. doi: 10.1090/proc/16948.
- .“The common basis complex and the partial decomposition poset.” International Mathematics Research Notices 2024, № 18 (): 12746–12760. doi: 10.1093/imrn/rnae177.
- .“A note on virtual duality and automorphism groups of right-angled Artin groups.” Glasgow Mathematical Journal 65, № 3 (): 573 –581. doi: 10.1017/s0017089523000149.
- .“Stratifying the space of barcodes using Coxeter complexes.” Journal of Applied and Computational Topology 7 (): 369–395. doi: 10.1007/s41468-022-00104-7.
- “Apartment classes of integral symplectic groups.” Journal of Topology and Analysis (): 2305.17697. doi: 10.1142/S1793525324500286. [accepted / in Press (not yet published)]
- .“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.
- .“Persistent homology in cosmic shear II. A tomographic analysis of DES-Y1.” Astronomy and Astrophysics 667 (): A125. doi: 10.1051/0004-6361/202243868.
- .“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.
- .“Persistent homology in cosmic shear: Constraining parameters with topological data analysis.” Astronomy and Astrophysics 648 (): A74. doi: 10.1051/0004-6361/202039048.
- .“The Farrell–Jones conjecture for normally poly-free groups.” Proceedings of the American Mathematical Society 149 (): 2349–2356. doi: 10.1090/proc/15357.
- .“Higher generating subgroups and Cohen–Macaulay complexes.” Proceedings of the Edinburgh Mathematical Society 63, № 1 (): 275–285. doi: 10.1017/S0013091519000415.
- .“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.
- .“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)
- . Between buildings and free factor complexes. Dissertation thesis, Universität Bielefeld. . N/A: Selbstverlag / Eigenverlag, .
Other Non-Scientific Publications
- . Über Brücken und Grenzen entlang der Donau. 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.