zum Hauptinhalt wechseln zum Hauptmenü wechseln zum Fußbereich wechseln Universität Bielefeld Play Search
zum Hauptinhalt wechseln
Breadcrumb überspringen und zum Hauptmenü wechseln

AG Voll

© Universität Bielefeld

Research

Research interests

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.

Click here for my CV (last updated in November 2024).

All publications in PUB

Preprints

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.

Selected Grants

  • SFB-TRR 358, principal Investigator within the projects A1 "The structure of (almost) lattices – algebra, analysis, and arithmetic", A4 "Combinatorial Euler products" and A6 "Zeta functions of integral quiver representations", since 2023, Bielefeld and Paderborn University.
  • DFG grant Order zeta functions and resolution of singularities (2017 - 20), jointly with A. Frühbis-Krüger, Hannover.
  • German-Israeli Foundation grant Subgroup and subring growth under base extension (2015 - 17), jointly with M. M. Schein, Bar-Ilan University, Israel.
  • Alexander von Humboldt Foundation, Feodor Lynen Research Fellowship (2015 - 17) to visit E. A. O'Brien, Auckland, NZ.
  • DFG Priority Programme "Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory" 1489 (Grant VO-1248/3-1 "Toroidal methods for computing zeta functions of groups and rings"), 07/2013 - 06/2016.
  • DFG Sonderforschungsbereich 701 (Projects C10 "Local cohomology and support in representation theory" (co-PI with Henning Krause) and C12 "Representation growth of arithmetic groups" (sole PI)), 07/2013 - 06/2017.
  • EPSRC Small Grant EP/H044779/1 (with B. Klopsch, PI) to collaborate with U. Onn, Ben-Gurion University of the Negev, Beersheva, Israel.
  • EPSRC Overseas Travel Grant EP/H044779/1 to visit E.A. O'Brien, Auckland, NZ.
  • EPSRC Small Grant EP/G055408/1 (with B. Klopsch) for workshop Representations and Asymptotic Group Theory, 6 - 7 April 2009 in Southampton.
  • EPSRC First Grant EP/F044194/1 "Zeta functions of groups and rings and Igusa's local zeta function", 04/2009 - 03/2012.
  • Nuffield Foundation Newly Appointed Lecturers Grant, 09/2006 - 04/2009.
  • Royal Society Outgoing Short Visits grant to visit E. O'Brien (Auckland, NZ) and B. Martin (Christchurch, NZ), 07/2008.
  • Fonds National Suisse Individual Short Visit to visit Laurent Bartholdi (then EPFL, Switzerland), 03 - 04/2006.
  • Max-Planck-Institut für Mathematik, Bonn, Weiterbildungsstipendium, 10/2005 - 03/2006.
  • Deutsche Forschungsgemeinschaft Forschungsstipendium, Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, 10/2004 - 09/2005.
  • EPSRC Postdoctoral Fellowship in Mathematics GR/R93827/01 "Bruhat - Tits buildings and functional equations of zeta functions of nilpotent groups", Mathematical Institute, University of Oxford, 10/2002 - 09/2004.

People

Postdocs

PhD students

Events

Meetings (co-)organised

Zum Seitenanfang