Tobias Rossmann


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 pro-p groups.

Research articles

Published or accepted for publication

  1. Periodicities for graphs of p-groups beyond coclass (with Bettina Eick). In Computational group theory and the theory of groups, II. Contemp. Math. 511 (2010), 11–23. (preprint)
  2. Irreducibility testing of finite nilpotent linear groups. J. Algebra 324 (2010), 1114–1124. (preprint)
  3. Primitivity testing of finite nilpotent linear groups LMS J. Comput. Math. 14 (2011), 87–98. (preprint)
  4. Computing topological zeta functions of groups, algebras, and modules, I. Proc. Lond. Math. Soc. (3) 110 (2015), no. 5, 1099–1134. (preprint)
  5. Computing topological zeta functions of groups, algebras, and modules, II. J. Algebra 444 (2015), 567–605. (preprint)
  6. Topological representation zeta functions of unipotent groups. J. Algebra 448 (2016), 210–237. (preprint)
  7. Primitive finite nilpotent linear groups over number fields. J. Algebra 451 (2016), 248–267. (preprint)
  8. Enumerating submodules invariant under an endomorphism. Math. Ann. 368 (2017), no. 1, 391–417. (preprint)
  9. Stability results for local zeta functions of groups, algebras, and modules, Math. Proc. Camb. Phil. Soc. (2017), 10 pages. (preprint)
  10. Computing local zeta functions of groups, algebras, and modules. Trans. Amer. Math. Soc. (2017), 42 pages. (preprint)

Submitted

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

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. 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

  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)

Software

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

Academic employment

since 2016 Feodor Lynen Postdoctoral Fellow (Alexander von Humboldt-Foundation), University of Auckland. Host: Eamonn O'Brien
2011–2016 Postdoc, Bielefeld University. DFG-funded project Toroidal methods for computing zeta functions of groups and rings (2013–2016) within the Priority Programme “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”. PI: Christopher Voll

Education

2017 Habilitation in Mathematics, Bielefeld University
2011 PhD in Mathematics, National University of Ireland, Galway
2008 Diplom in Mathematics, Technische Universität Braunschweig

Teaching

University of Auckland

  1. Discrete Structures in Mathematics and Computer Science (COMPSCI 225) (Semester 2, 2017)
  2. Group Theory (MATHS 720) (Semester 1, 2017)

Bielefeld University

  1. Elementare Zahlentheorie (4+2) (SS 2016)
  2. Geometrie von Gröbnerbasen (2+2) (SS 2013)
  3. Algorithmische Algebra (2+2) (WS 2012/2013)

Contact

Tobias Rossmann
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland
New Zealand

E-mail: tobias.rossmann (at) googlemail.com

last modified: 27 September 2017