Christopher Voll, PhD (cantab)

CV at work

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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

Elsevier boycott

I joined a number of researchers - more than 19.000 as of July 2021 - in boycotting Elsevier, the academic publisher; see The Cost of Knowledge for background.


Click here for a 8-page CV (last updated in April 2021).


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.

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.


  1. Flag Hilbert-Poincare series of hyperplane arrangements and their Igusa zeta functions, with J. Maglione, arxiv, 48 pages.
  2. Zeta functions of integral nilpotent quiver representations, with S. Lee, arxiv, 31 pages.
  3. Generalized Igusa functions and ideal growth in nilpotent Lie rings, with A. Carnevale and M. M. Schein, arxiv, 34 pages (extended abstract (FPSAC 2020)).

Book chapters

  1. Zeta functions of groups and rings - recent developments, in Groups St Andrews 2013 in St Andrews, editors C. M. Campbell, M. R. Quick, E.F. Robertson, C. M. Roney-Dougal, London Math. Soc. Lecture Note Ser. 422, 469--492, Cambridge Univ. Press, Cambridge, 2015, CUP
  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 Math. Soc. Stud. Texts 77, 99-144, Cambridge Univ. Press, Cambridge, 2011, CUP
  3. Zeta functions of groups and rings - functional equations and analytic uniformity, in Spectral Structures and Topological Methods in Mathematics, editors M. Baake, F. Götze, W. Hoffmann, EMS Series of Congress reports 13 (2019), 345--363, AMS bookstore.

Papers (published or accepted for publication)

  1. Groups, graphs, and hypergraphs: average sizes of kernels of generic matrices with support constraints, with T. Rossmann, to appear in Memoirs of the Amer. Math. Soc., arxiv, 109 pages.
  2. Hessian matrices, automorphisms of p-groups, and torsion points of elliptic curves, with M. Stanojkovski, to appear in Math. Ann., pdf.
  3. Ideal zeta functions associated to a family of class-2-nilpotent Lie rings, The Quarterly Journal of Mathematics (2020), pdf.
  4. Enumerating graded ideals in graded rings associated to free nilpotent Lie rings, with S. Lee, Math. Z. 290 (2018), 1249--1276, pdf, arxiv
  5. Enumerating traceless matrices over compact discrete valuation rings, with A. Carnevale and S. Shechter, Israel J. Math. 227 (2018), 956--986, pdf, arxiv
  6. Orbit Dirichlet series and multiset permutations, with A. Carnevale, Monatsh. Math. 186 (2018), 215--233, pdf, arxiv
  7. Local functional equations for submodule zeta functions associated to nilpotent algebras of endomorphisms, Int. Math. Res. Not. IMRN (2017), pdf, arxiv
  8. Representation zeta functions of some nilpotent groups associated to prehomogenous vector spaces, with A. Stasinski, Forum Math. 29 (2017), 717--734, pdf, arxiv,
  9. 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,
  10. 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
  11. 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.
  12. Enumerating classes and characters of p-groups, with E. A. O'Brien, Trans. Amer. Math. Soc. 367 (2015), 7775 -- 7796, pdf, arxiv
  13. 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
  14. 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
  15. 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
  16. A New Statistic on the Hyperoctahedral Groups, with A. Stasinski, Electron. J. Combin. 20, issue 3 (2013), P50, pdf, arxiv
  17. 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
  18. 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
  19. Functional equations for zeta functions of groups and rings, Ann. Math. 172 (2010), 1181--1218, pdf, arxiv
  20. 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
  21. Enumerating finite class-2-nilpotent groups on 2 generators, C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 1347-1350, pdf, arxiv
  22. Zeta function of 3-dimensional p-adic Lie algebras, with B. Klopsch, Math. Z. 263, No. 1 (2009), 195--210, pdf, arxiv
  23. 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
  24. 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
  25. Counting subgroups in a family of nilpotent semidirect products, Bull. London Math. Soc., No. 38 (2006), 743--752, pdf, arxiv
  26. Normal subgroup growth in free class-2-nilpotent groups, Math. Ann. 332, No. 1 (2005), 67--79, pdf, arxiv
  27. 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
  28. Zeta functions of groups and enumeration in Bruhat-Tits buildings, Amer. J. Math. 126 (2004), 1005--1032, pdf, arxiv

Selected grants

Meetings (co-)organised


PhD students

Teaching (in German)

Sommersemester 2021

Wintersemester 2020/21

Sommersemester 2020

Wintersemester 2019/20

Sommersemester 2019

Forschungsfreisemester (sabbatical)

Wintersemester 2018/19

Sommersemester 2018

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: 28 July 2021