Christopher Voll, PhD (cantab)

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Prof. Dr. Christopher Voll

Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
D-33501 Bielefeld
Telephone: 0049-521-1065025
Telephone (secretary Ms Nopto): 0049-521-1065021
Email: surname at math dot uni minus bielefeld dot de

Postdoc position

There is currently a postdoc position available in my research group; see here for details.

Elsevier boycott

I joined a number of researchers - more than 16.700 as of July 2017 - in boycotting Elsevier, the academic publisher; see The Cost of Knowledge for background.


I coordinate the Mathematisches Kolloquium at Bielefeld.


Click here for a 8-page CV (last updated in July 2017).


My research interests are centred around asymptotic group theory, in particular arithmetic and analytic properties of zeta functions associated to infinite groups and rings. These are Dirichlet generating functions encoding arithmetic data about groups and rings, such as the numbers of finite index subobjects or finite-dimensional irreducible representations. The study of these zeta functions may be seen as a non-commutative analogue to the theory of the Dedekind zeta function of a number field, enumerating finite index ideals in the number field's ring of integers. This young subject area lies on the crossroads of infinite group and ring theory, algebraic geometry and combinatorics. I have written "A newcomer's guide to zeta functions of groups and rings", see here.

I welcome enquiries about possible PhD projects from suitably qualified candidates. I am also happy to consider sponsoring postdoc applications, e.g. under the Marie Curie Actions or the Alexander von Humboldt Foundation's schemes.

Papers (submitted for publication)

  1. Enumerating traceless matrices over compact discrete valuation rings, with A. Carnevale and S. Shechter, arxiv, 20 pages.
  2. Orbit Dirichlet series and multiset permutations, with A. Carnevale, arxiv, 13 pages.
  3. Enumerating graded ideals in graded rings associated to free nilpotent Lie rings, with S. Lee, arxiv, 28 pages.

Book chapters

  1. Zeta functions of groups and rings - recent developments. A survey based on a talk at the conference Groups St Andrews 2013, to appear in the conference's proceedings volume, arxiv
  2. A newcomer's guide to zeta functions of groups and rings, in B. Klopsch, N. Nikolov, C. Voll, Lectures on profinite topics in group theory, editor D. Segal, London Mathematical Society Student Texts 77, Cambridge University Press, 2011, CUP, arxiv

Papers (published or accepted for publication)

  1. Local functional equations for submodule zeta functions associated to nilpotent algebras of endomorphisms, Int. Math. Res. Not. IMRN (2017), pdf, arxiv
  2. Representation zeta functions of some nilpotent groups associated to prehomogenous vector spaces, with A. Stasinski, Forum Math. 29 (2017), 717--734, pdf, arxiv,
  3. Uniform analytic properties of representation zeta functions of finitely generated nilpotent groups, with Duong H. D., in Trans. Amer. Math. Soc. 369 (2017), 6327--6349, pdf, arxiv,
  4. Arithmetic groups, base change, and representation growth, with N. Avni, B. Klopsch and U. Onn, Geom. Func. Anal. (GAFA) 26 (2016), 67--135, pdf, arxiv
  5. Similarity classes of integral p-adic matrices and representation zeta functions of groups of type A_2, with N. Avni, B. Klopsch and U. Onn, Proc. Lond. Math. Soc. (3) 112 (2016), no. 2, 267 -- 350, pdf, arxiv.
  6. Enumerating classes and characters of p-groups, with E. A. O'Brien, Trans. Amer. Math. Soc. 367 (2015), 7775 -- 7796, pdf, arxiv
  7. Normal zeta functions of the Heisenberg groups over number rings I - the unramified case, with M. M. Schein, J. Lond. Math. Soc. 91 (2014), 19 -- 46, pdf, arxiv
  8. Normal zeta functions of the Heisenberg groups over number rings II - the non-split case, with M. M. Schein, Israel J. Math. 211 (2016), no. 1, 171 -- 195, pdf, arxiv
  9. Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B, with A. Stasinski, Amer. J. Math. 136 (2014), 501 -- 550, pdf, arxiv
  10. A New Statistic on the Hyperoctahedral Groups, with A. Stasinski, Electron. J. Combin. 20, issue 3 (2013), P50, pdf, arxiv
  11. Representation zeta functions of compact p-adic analytic groups and arithmetic groups, with N. Avni, B. Klopsch and U. Onn, Duke Math. J. 162 (2013), 111-197, pdf, arxiv
  12. Representation zeta functions of some compact p-adic analytic groups, with N. Avni, B. Klopsch and U. Onn, Cont. Math. 566 (2012), 295-330, arxiv
  13. Functional equations for zeta functions of groups and rings, Ann. Math. 172 (2010), 1181--1218, pdf, arxiv
  14. On representation zeta functions of groups and a conjecture of Larsen-Lubotzky, with N. Avni, B. Klopsch and U. Onn, C. R. Math. Acad. Sci. Paris, Ser. I 348 (2010), 363--367, pdf, arxiv
  15. Enumerating finite class-2-nilpotent groups on 2 generators, C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 1347-1350, pdf, arxiv
  16. Zeta function of 3-dimensional p-adic Lie algebras, with B. Klopsch, Math. Z. 263, No. 1 (2009), 195--210, pdf, arxiv
  17. Igusa-type functions associated to finite formed spaces and their functional equations, with B. Klopsch, Trans. Amer. Math. Soc. 361 (2009), 4405--4436, pdf, arxiv
  18. Zeta functions of groups - singular pfaffians, in Essays in Geometric Group Theory, editor N. S. N. Sastry, Ramanujan Mathematical Society Lecture Notes Series, No. 9, 2009, arxiv
  19. Counting subgroups in a family of nilpotent semidirect products, Bull. London Math. Soc., No. 38 (2006), 743--752, pdf, arxiv
  20. Normal subgroup growth in free class-2-nilpotent groups, Math. Ann. 332, No. 1 (2005), 67--79, pdf, arxiv
  21. Functional equations for local normal zeta functions of nilpotent groups, with an appendix by A. Beauville, Geom. Func. Anal. (GAFA) 15 (2005), 274--295, pdf, arxiv
  22. Zeta functions of groups and enumeration in Bruhat-Tits buildings, Amer. J. Math. 126 (2004), 1005--1032, pdf, arxiv

Selected grants

Meetings organised


PhD students

Teaching (in German)

Wintersemester 2017/18

Sommersemester 2017

Wintersemester 2016/17

Sommersemester 2016

Wintersemester 2015/16

Sommersemester 2015

Wintersemester 2014/15

Sommersemester 2014

Forschungsfreisemester (sabbatical)

Wintersemester 2013/14

Sommersemester 2013

Wintersemester 2012/13

Sommersemester 2012

Wintersemester 2011/12


Ich bin einer der Unterschriftsberechtigten der Fakultät für Mathematik für Leistungsbescheinigungen nach § 48 BAföG. Wenn Sie wünschen, dass ich eine solche Bescheinigung ausstelle, lesen Sie bitte diese Hinweise. Die fakultätsinternen Richtlinien für die Bewertung von Leistungen für diese Zwecke finden Sie hier.

Last updated: 17 October 2017