Tobias Rossmann
About
I am a postdoc in the Department of Mathematics at
the University of Auckland,
funded primarily by the Alexander von Humboldt Foundation.
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 or
representations of nilpotent groups.
I have also worked on and remain interested in classification and counting
problems for nilpotent and prop groups.
Research articles
Published or accepted for publication

Periodicities for graphs of pgroups beyond coclass
(with Bettina Eick).
In Computational group theory and the theory of groups, II.
Contemp. Math. 511 (2010), 11–23.
(preprint)

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)

Stability results for local zeta functions of groups, algebras, and
modules,
Math. Proc. Camb. Phil. Soc. (2017), 10 pages.
(preprint)
 Computing local zeta functions of groups, algebras, and modules.
Trans. Amer. Math. Soc. (2017), 42 pages.
(preprint)
Submitted

The average size of the kernel of a matrix and orbits of linear groups.
38 pages.
(preprint)
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)

A framework for computing zeta functions of groups, algebras, and
modules.
To appear in Algorithmic and Experimental Methods in Algebra, Geometry and
Number Theory, 27 pages.
(preprint)
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)
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).
Academic employment
Education
Teaching
University of Auckland
 Discrete Structures in Mathematics and Computer Science
(COMPSCI 225) (Semester 2, 2017)
 Group Theory (MATHS 720) (Semester 1, 2017)
Bielefeld University
 Elementare Zahlentheorie (4+2) (SS 2016)
 Geometrie von Gröbnerbasen (2+2) (SS 2013)
 Algorithmische Algebra (2+2) (WS 2012/2013)
Contact
Tobias Rossmann
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland
New Zealand
Email: tobias.rossmann (at) googlemail.com
last modified: 27 September 2017