Robin J. Sroka

I am a mathematician and Postdoctoral Research Associate at the University of Münster working in the research areas ``Arithmetic and Groups'' and ``Spaces and Operators''. I am an investigator at the Cluster of Excellence ``Mathematics Münster'' and a member of the Collaborative Research Centre ``Geometry: Deformations and Rigidity''.

From September 2021 to August 2023, I was a Postdoctoral Fellow in the ``Geometry & Topology'' group at McMaster University working under the mentorship of Ian Hambleton. From January to April 2022, I participated in the research program ``Higher algebraic structures in algebra, topology and geometry'' at Institut Mittag-Leffler as a Junior Fellow. In September 2021, I completed my PhD studies at the University of Copenhagen under the supervision of Nathalie Wahl.

Contact

Mathematisches Institut
Universität Münster
Einsteinstrasse 62
48149 Münster, Germany

Office 513

robinjsroka[at]uni-muenster.de

Research

I am interested in algebraic topology, geometric group theory, and geometric topology as well as connections to number theory and dynamics.

My research explores patterns in (co)homological invariants of groups and algebras, often in relation to questions in (algebraic) K-theory. This usually relies on a good understanding of combinatorial geometries and simplicial structures on which the groups and algebras act.

My PhD thesis, ``Patterns in the homology of algebras: Vanishing, stability, and higher structures'', is available here.

At the Cluster of Excellence ``Mathematics Münster'', I work as an investigator within the research group ``K-Groups and cohomology''. My co-author Benjamin Brück and I form the Young Research Group ``High-dimensional cohomology of arithmetic groups''.

Activities & Organization

• I am co-organizing Groups and Geometry in North Rhine-Westphalia; a series of one-day meetings, with the aim of bringing together geometric group theorists, topologists, and geometers. The next meeting is scheduled for April 25, 2025 and will take place at the University of Münster.
• I am co-organizing the workshop Perspectives on the cohomology of general linear groups, which will take place from October 6 to October 10, 2025 at the University of Münster.
• I am co-organizing the Oberseminar Topologie during the Winter Term 2024.
• I am participating in a Learning seminar on topological and measurable full groups during the Winter Term 2024.

Publications & Preprints

1. Scissors automorphism groups and their homology.
   ‣ with Alexander Kupers, Ezekiel Lemann, Cary Malkiewich, and Jeremy Miller.
   ‣ arXiv, Aug 2024.
2. Partial bases and homological stability of GL_n(R) revisited.
   ‣ with Calista Bernard and Jeremy Miller.
   ‣ arXiv, May 2024.
3. Simplicial bounded cohomology and stability.
   ‣ with Thorben Kastenholz.
   ‣ arXiv, Sep 2023.
4. A presentation of symplectic Steinberg modules and cohomology of Sp_2n(ℤ).
   ‣ with Benjamin Brück and Peter Patzt.
   ‣ arXiv, Jun 2023.
5. Apartment classes of integral symplectic groups.
   ‣ with Benjamin Brück.
   ‣ Published in Journal of Topology and Analysis.
   ‣ arXiv, May 2023. Journal, Dec 2024.
6. On the top-dimensional cohomology of arithmetic Chevalley groups.
   ‣ with Benjamin Brück and Yuri Santos Rego.
   ‣ Published in Proceedings of the American Mathematical Society.
   ‣ arXiv, Oct 2022. Journal, Aug 2024.
7. On the codimension-two cohomology of SL_n(ℤ).
   ‣ with Benjamin Brück, Jeremy Miller, Peter Patzt and Jennifer C. H. Wilson.
   ‣ Published in Advances in Mathematics.
   ‣ arXiv, Apr 2022. Journal, Jun 2024.
8. The homology of a Temperley-Lieb algebra on an odd number of strands.
   ‣ Published in Algebraic & Geometric Topology.
   ‣ arXiv, Feb 2022. Journal, Oct 2024.

Talks & Travel

• TBA.
  ‣ May 6, 2025. Online Talk, South Atlantic Noncommutative Geometry Seminar (GeNoCAS), Universidad de Buenos Aires.
• Scissors automorphism groups and their homology.
  ‣ Jan 30, 2025. Après-midi de topologie, Université Paris Cité.
• On Szőke's Tits alternative for topological full groups.
  ‣ Jan 27, 2025. Expository talk, Learning seminar on topological and measurable full groups, University of Münster.
• K-theory, scissors congruence and dynamics.
  ‣ Jan 7, 2025. Oberseminar C*-Algebren, Universität Münster.
• K-theory, scissors congruence and dynamics.
  ‣ Nov 28, 2024. Analysis Seminar, University of Glasgow.
• Scissors automorphism groups and their homology.
  ‣ Nov 27, 2024. Differential Geometry & Topology Seminar, University of Cambridge.
• Homological stability: From algebraic K-theory to bounded cohomology, scissors congruence and dynamics.
  ‣ Jul 23, 2024. Geometry and Topology Seminar, McMaster University.
• Scissors automorphism groups and their homology.
  ‣ Jul 9, 2024. ``Scissors congruences, algebraic K-theory and Steinberg modules'', American Institute of Mathematics.
• Homological stability and K-theory.
  ‣ Jun 14, 2024. Oberseminar Algebra und Geometrie, Heinrich Heine University Düsseldorf.
• Homological stability and K-theory.
  ‣ Jun 13, 2024. Wilhelm Killing Kolloquium: Postdocs of Mathematics Münster, University of Münster.
• High-dimensional rational cohomology of arithmetric groups I & II.
  ‣ May 28 and Jun 4, 2024. Mittagsseminar zur Arithmetik, University of Münster.
  ‣ with Benjamin Brück.
• Homological stability, K-theory and topological full groups: On recent work of Xin Li.
  ‣ May 27, 2024. Expository talk, Kleines Seminar, University of Münster.
• High-dimensional cohomology of arithmetic Chevalley groups.
  ‣ Mar 25, 2024. Poster at ``Mathematics Münster Mid-term Conference'', University of Münster.
  ‣ with Benjamin Brück.
• Simplicial bounded cohomology and stability.
  ‣ Feb 8, 2024. AG Algebraic and Geometric Topology, Karlsruhe Institute of Technology.
• Steinberg modules and (co-)homology of arithmetic groups.
  ‣ Jan 16, 2024. Topological Activities, Stockholm University.
• Simplicial bounded cohomology and stability.
  ‣ Dec 11, 2023. Online Talk, IYSBC-SV Seminar.
• Steinberg modules and high-dimensional rational cohomology of symplectic groups.
  ‣ Nov 8, 2023. Algebra and Number Theory Seminar, University of Glasgow.
• Steinberg modules and high-dimensional rational cohomology of symplectic groups.
  ‣ Oct 25, 2023. Oberseminar Topologie, University of Münster.
• Simplicial bounded cohomology and stability.
  ‣ Jul 20, 2023. ``Stability in Topology, Arithmetic, and Representation Theory 2023'', Purdue University.
• On the high-dimensional rational cohomology of arithmetic Chevalley groups.
  ‣ Apr 13, 2023. Topology Seminar, University of Michigan.
• On the high-dimensional rational cohomology of arithmetic Chevalley groups.
  ‣ Dec 19, 2022. Online talk, COGENT Seminar.
• On the high-dimensional rational cohomology of arithmetic Chevalley groups.
  ‣ Dec 5, 2022. Online talk, Topology Seminar, University of Minnesota.
• Partial bases and homological stability for general linear groups revisited.
  ‣ Oct 12, 2022. Purdue Topology Seminar, Purdue University.
• The homology of a Temperley-Lieb algebra on an odd number of strands.
  ‣ Mar 23, 2022. Online talk, IMUNAM Algebraic Topology Seminar, National Autonomous University of Mexico.
• On the high-dimensional rational cohomology of special linear groups.
  ‣ Jan 21, 2022. ``Higher algebraic structures in algebra, topology and geometry'', Institut Mittag-Leffler.
• Patterns in the homology of Iwahori-Hecke algebras.
  ‣ Dec 14, 2021. Geometry and Topology Seminar, McMaster University.
• On the high-dimensional rational cohomology of special linear groups.
  ‣ Nov 1, 2021. Geometry & Topology Seminar, University of Toronto.
• On the high-dimensional rational cohomology of symplectic groups.
  ‣ Jul 1, 2021. ``High dimensional cohomology of moduli spaces'', University of Copenhagen.
• Algebraic analogues of coset posets and the low dimensional homology of Iwahori-Hecke algebras.
  ‣ Aug 21, 2020. ``Simplicial complexes workshop'', University of Copenhagen.

Mar 13, 2025