Tobias Rossmann

About

I am a Lecturer in Mathematics in the School of Mathematical and Statistical Sciences at the University of Galway.

Research interests

My research is in the field of algebra, mostly of the asymptotic or computational kind. In recent years, my main focus has been on zeta functions arising from algebraic counting problems such as the enumeration of subgroups, representations, linear orbits, or conjugacy classes.

Papers

Journal articles

1. Irreducibility testing of finite nilpotent linear groups. J. Algebra 324 (2010), 1114–1124. (preprint)
2. Primitivity testing of finite nilpotent linear groups. LMS J. Comput. Math. 14 (2011), 87–98. (preprint)
3. Computing topological zeta functions of groups, algebras, and modules, I. Proc. Lond. Math. Soc. (3) 110 (2015), no. 5, 1099–1134. (preprint)
4. Computing topological zeta functions of groups, algebras, and modules, II. J. Algebra 444 (2015), 567–605. (preprint)
5. Topological representation zeta functions of unipotent groups. J. Algebra 448 (2016), 210–237. (preprint)
6. Primitive finite nilpotent linear groups over number fields. J. Algebra 451 (2016), 248–267. (preprint)
7. Enumerating submodules invariant under an endomorphism. Math. Ann. 368 (2017), no. 1, 391–417. (preprint, view online)
8. Computing local zeta functions of groups, algebras, and modules. Trans. Amer. Math. Soc. 370 (2018), no. 7, 4841–4879. (preprint)
9. The average size of the kernel of a matrix and orbits of linear groups. Proc. Lond. Math. Soc. (3) 117 (2018), no. 3, 574–616. (preprint)
10. Stability results for local zeta functions of groups, algebras, and modules. Math. Proc. Camb. Phil. Soc. 165 (2018), no. 3, 435–444. (preprint)
11. The average size of the kernel of a matrix and orbits of linear groups, II: duality. J. Pure Appl. Algebra 224 (2020), no. 4, 106203, 28 pages. (preprint)
12. Enumerating conjugacy classes of graphical groups over finite fields. Bull. Lond. Math. Soc. 54 (2022), no. 5, 1923–1943. (preprint)
13. Linear relations with disjoint supports and average sizes of kernels (with Angela Carnevale). J. Lond. Math. Soc. 106 (2022), no. 3, 1759–1809. (preprint)
14. Groups, graphs, and hypergraphs: average sizes of kernels of generic matrices with support constraints (with Christopher Voll). Mem. Amer. Math. Soc. 294 (2024), no. 1465, vi+120 pp. (preprint)
15. On the enumeration of orbits of unipotent groups over finite fields. To appear in Proc. Amer. Math. Soc., 15 pages. (preprint)

Book chapters and conference proceedings

16. Periodicities for graphs of p-groups beyond coclass (with Bettina Eick). In: Kappe et al. (eds), Computational group theory and the theory of groups, II. Contemp. Math. 511 (2010), 11–23. (preprint)
17. A Framework for Computing Zeta Functions of Groups, Algebras, and Modules. In: Böckle et al. (eds), Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory (2017), Springer-Verlag, 561–586. (preprint)
18. From coloured permutations to Hadamard products and zeta functions (with Angela Carnevale and Vassilis Dionyssis Moustakas). Proceedings of the 36th Conference on Formal Power Series and Algebraic Combinatorics (Bochum). Séminaire Lotharingien de Combinatoire 91B (2024). Article #56, 12 pp. (preprint)

Preprints

19. Coloured shuffle compatibility, Hadamard products, and ask zeta functions (with Angela Carnevale and Vassilis Dionyssis Moustakas), 19 pages. (preprint)

Software

1. Zeta — computing zeta functions of groups, algebras, and modules (2014–present).
2. fwtree — computing trees related to some pro-p-groups of finite width (with Bettina Eick) (2009–2020).
3. finn — computing with finite nilpotent linear groups (2010–2011).

Database

A database of ask zeta functions associated with small graphs (see [12]) is available here.

Theses

1. p-Groups: Rank, Width, and Obliquity. Diploma thesis, TU Braunschweig (2007).
2. Algorithms for Nilpotent Linear Groups. PhD thesis, NUI Galway (2011). (PDF)
3. Zeta Functions of Groups, Algebras, and Modules. Habilitation thesis, Bielefeld University (2017). (Title page and introduction: PDF)

Reports

1. Computing with nilpotent linear groups. Oberwolfach Reports 8 (2011), no. 3, Computational Group Theory, 2121. (preprint)
2. Computing zeta functions of groups, algebras, and modules. Oberwolfach Reports 13 (2016), no. 3, Computational Group Theory, 2144–2145. (preprint)
3. Towards a symbolic enumeration of orbits. Oberwolfach Reports 38/2021, Computational Group Theory, 2064–2066. (preprint)

Selected talks and lectures

• Lectures given at the workshop “Zeta functions of groups and dynamical systems” in Düsseldorf (Germany), 17–20 September 2018:
  • Orbits, kernels, and growth of class numbers.
  • An introduction to Zeta. (notebook)
• Slides of a talk on Growth of class numbers of unipotent groups given at the workshop “Computational and algorithmic methods” as part of the programme on “Groups, representations and applications: new perspectives” at the Isaac Newton Institute for Mathematical Sciences (UK), 27–31 January 2020.
• Workshop course on “Enumerating orbits of groups” within the programme “Combinatorial methods in enumerative algebra” at the International Centre for Theoretical Sciences in Bengaluru (India), 2–13 December 2024.

Academic employment

Education

Conferences organised

1. Groups in Galway 2024 (with Angela Carnevale and Joshua Maglione), 16–17 May 2024.
2. Groups in Galway meets the Irish Geometry Conference (with John Burns, Angela Carnevale, and Martin Kerin), 18–20 May 2022.
3. Groups in Galway 2021 (with Angela Carnevale), 2–3 December 2021.
4. Groups in Galway 2020 - Online edition (with Angela Carnevale), 9–11 September 2020.
5. Groups in Galway 2019 (with Graham Ellis), 10–11 May 2019.
6. Groups in Galway 2018 (with Dane Flannery and Kevin Jennings), 18–19 May 2018.

Editorial work

I am a member of the Editorial Board of Experimental Mathematics.

PhD supervision

1. Sultan M. Alzahrani (2018–2022). Thesis: Explicit Computations of Ask Zeta Functions.
2. David Cormican (since 2023)
3. Mario Falciatore (co-supervised by Angela Carnevale, since 2024)
4. Lucrezia Prosperi (co-supervised by Angela Carnevale, since 2024)

Teaching 2024/2025

1. Logic (CS3304) (Semester 1)
2. Mathematics for Decision Making II (MA438) (Semester 2)
3. Topology (MA342) (Semester 2)

Contact

Tobias Rossmann
School of Mathematical and Statistical Sciences
University of Galway
Galway
H91 TK33
Ireland

Office: Áras de Brún, room ADB-1006
Phone: +353 91 492043
E-mail: tobias.rossmann (at) universityofgalway.ie