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, or conjugacy classes.
Papers
Journal articles

Irreducibility testing of finite nilpotent linear groups.
J. Algebra 324 (2010), 1114–1124.
(preprint)

Primitivity testing of finite nilpotent linear groups.
LMS J. Comput. Math. 14 (2011), 87–98.
(preprint)

Computing topological zeta functions of groups, algebras, and
modules, I.
Proc. Lond. Math. Soc. (3) 110 (2015), no. 5, 1099–1134.
(preprint)

Computing
topological zeta functions of groups, algebras, and modules, II.
J. Algebra 444 (2015), 567–605.
(preprint)

Topological representation zeta functions of unipotent groups.
J. Algebra 448 (2016), 210–237.
(preprint)

Primitive finite nilpotent linear groups over number fields.
J. Algebra 451 (2016), 248–267.
(preprint)

Enumerating submodules invariant under an endomorphism.
Math. Ann. 368 (2017), no. 1,
391–417. (preprint,
view online)
 Computing local zeta functions of groups, algebras, and modules.
Trans. Amer. Math. Soc. 370 (2018), no. 7, 4841–4879.
(preprint)

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)

Stability results for local zeta functions of groups, algebras, and modules.
Math. Proc. Camb. Phil. Soc. 165 (2018), no. 3, 435–444.
(preprint)

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)

Enumerating conjugacy classes
of graphical groups over finite fields.
Bull. Lond. Math. Soc. 54 (2022), no. 5, 1923–1943. (preprint)

Linear relations with disjoint supports and average sizes of kernels.
(with Angela Carnevale).
J. Lond. Math. Soc. 106 (2022), no. 3, 1759–1809. (preprint)

Groups, graphs, and hypergraphs: average sizes of kernels of generic
matrices with support constraints
(with Christopher
Voll).
To appear in Mem. Amer. Math. Soc.,
114 pages. (preprint)
Book chapters

Periodicities for graphs of pgroups 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)

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), SpringerVerlag, 561–586.
(preprint)
Preprints

On the enumeration of orbits of unipotent groups over finite
fields, 15 pages. (preprint)
Software

fwtree — computing trees related to some propgroups of finite width (with Bettina Eick) (2009).
 finn — computing with finite nilpotent linear groups (2010–2011).
 Zeta — computing zeta functions of groups, algebras,
and modules (2014–present).
Data
A list of ask zeta functions associated with small graphs (see [12]) is available here.
Theses
 pGroups: Rank, Width, and Obliquity.
Diploma thesis, TU Braunschweig (2007).
 Algorithms for Nilpotent Linear Groups.
PhD thesis, NUI Galway (2011).
(PDF)
 Zeta Functions of Groups, Algebras, and Modules.
Habilitation thesis, Bielefeld University (2017).
(Title page and introduction: PDF)
Reports

Computing with nilpotent
linear groups.
Oberwolfach Reports 8 (2011), no. 3,
Computational Group Theory, 2121.
(preprint)

Computing zeta
functions of groups, algebras, and modules.
Oberwolfach Reports 13 (2016), no. 3,
Computational Group Theory, 2144–2145.
(preprint)

Towards a symbolic enumeration of orbits.
Oberwolfach Reports 38/2021,
Computational Group Theory.
(preprint)
Selected talks
Academic employment
Education
Conferences organised

Groups in Galway meets the Irish Geometry Conference
(with John Burns,
Angela Carnevale, and
Martin Kerin),
18–20 May 2022.

Groups in Galway 2021 (with Angela Carnevale),
2–3 December 2021.

Groups in Galway 2020  Online edition (with Angela Carnevale),
9–11 September 2020.

Groups in Galway 2019
(with Graham Ellis), 10–11
May 2019.

Groups in Galway 2018 (with Dane Flannery and Kevin Jennings), 18–19 May 2018.
Teaching 2022/2023
 Logic (CS3304) (Semester 1)
 Rings (MA416) (Semester 1)
 Mathematics for Decision Making I (MA437) (Semester 1)
Contact
Tobias Rossmann
School of Mathematical and Statistical Sciences
University of Galway
Galway
H91 TK33
Ireland
Office: Áras de Brún, room ADB1006
Phone: +353 91 492043
Email: tobias.rossmann (at) universityofgalway.ie
last modified: 18 October 2022