Forschungsschwerpunkte
Geometrische Gruppentheorie
Gruppen sind algebraische Strukturen die verwendet werden um Symmetrien zu beschreiben. Sie sind die zentralen Objekte meiner Forschung. Um sie besser zu verstehen nutze ich oft topologische Methoden, aber z.B. auch Werkzeuge aus Kombinatorik, Wahrscheinlichkeitstheorie und Logik.
Vita
Akademische Ausbildung
- Promotion Mathematik, Universität Bielefeld
- Master in Mathematik, Universität Münster
- Bachelor in Mathematik, Universität Münster
Beruflicher Werdegang
- Akademischer Rat auf Zeit, Universität Münster
- Wissenschaftlicher Mitarbeiter, Universität Münster
- Hermann-Weyl-Instructor, ETH Zürich
- Postdoctoral researcher, University of Copenhagen
Mitgliedschaft oder Aktivität in einem Gremium
- Mathematics Münster (Young Research Group - "High-dimensional cohomology of arithmetic groups", Investigator)
Publikationen
Forschungsartikel in Online-Sammlungen
- . The common basis complex and the partial decomposition poset. arXiv, . doi: 10.48550/arXiv.2402.10484. [submitted / under review]
- . (Non-)Vanishing of high-dimensional group cohomology. arXiv, . doi: 10.48550/arXiv.2404.15026. [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]
- 10.48550/arXiv.2306.03180. [submitted / under review] A presentation of symplectic Steinberg modules and cohomology of Sp_2n(Z). arXiv, . doi:
- 10.48550/arXiv.2204.11967. [submitted / under review] On the codimension-two cohomology of SL_n(Z). arXiv, . doi:
Forschungsartikel (Zeitschriften)
- . “Median quasimorphisms on CAT(0) cube complexes and their cup products.” Geometriae Dedicata 218 (): 28. doi: 10.1007/s10711-023-00870-3.
- 10.48550/arXiv.2210.12784. [accepted / in Press (not yet published)] “On the top-dimensional cohomology of arithmetic Chevalley groups.” Proceedings of the American Mathematical Society (): 2210.12784. doi:
- . “A note on virtual duality and automorphism groups of right-angled Artin groups.” Glasgow Mathematical Journal 65, No. 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.
- 10.48550/arXiv.2305.17697. [accepted / in Press (not yet published)] “Apartment classes of integral symplectic groups.” Journal of Topology and Analysis (): 2305.17697. doi:
- . “Between buildings and free factor complexes: A Cohen–Macaulay complex for Out(RAAGs).” Journal of the London Mathematical Society 105, No. 1 (): 251–307. doi: 10.1112/jlms.12511.
- . “A Central Limit Theorem for the Two-Sided Descent Statistic on Coxeter Groups.” Electronic Journal of Combinatorics 29, No. 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.
- . “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, No. 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, No. 6 (): 1737–1765. doi: 10.1112/plms.12381.
- . “Maximal hyperbolic towers and weight in the theory of free groups.” Mathematical Proceedings 170, No. 3 (): 479–498. doi: 10.1017/S0305004119000483.
Qualifikationsschriften (Dissertationen, Habilitationsschriften)
- . Between buildings and free factor complexes. Dissertationsschrift, Universität Bielefeld. . Bielefeld: Selbstverlag / Eigenverlag / Self-publishing , .
Sonstige nicht-wissenschaftliche Veröffentlichungen
- . Über Brücken und Grenzen entlang der Donau. readbox unipress, .
Dr. Benjamin Brück
Code
Zusätzlich zu den Veröffentlichungen oben enthält meine Github Seite öffentlich verfügbaren Code, den ich in Forschungsprojekten verwendet habe.
Young Research Group
Robin J. Sroka und ich bilden die Young Research Group "High-dimensional cohomology of arithmetic groups" am Exzellenzcluster Mathematik Münster.