Christopher Voll, PhD (cantab)
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Contact
Prof. Dr. Christopher Voll
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
D-33501 Bielefeld
Germany
Telephone: 0049-521-1065025
Telephone (secretary Ms Nopto): 0049-521-1065021
Email: surname at math dot uni minus bielefeld dot de
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Elsevier boycott
I joined a number of researchers - more than 17.600 as of August 2019 -
in boycotting Elsevier, the academic publisher;
see The Cost of Knowledge
for background.
CV
Click here for a 8-page CV (last updated
in March 2019).
Research
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.
Preprints
- Zeta functions of integral nilpotent quiver representations, with
S. Lee, arxiv, 31 pages.
- Hessian matrices, automorphisms of p-groups, and torsion points
of elliptic curves, with
M. Stanojkovski, arxiv, 26
pages.
- Groups, graphs, and hypergraphs: average sizes of kernels of generic
matrices with support constraints, with
T. Rossmann, arxiv, 109 pages.
- Generalized Igusa functions and ideal growth in nilpotent Lie rings,
with A. Carnevale and
M. M. Schein, arxiv, 34
pages.
Book chapters
- 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
- 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
- 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)
- Ideal zeta functions associated to a family of class-2-nilpotent Lie
rings, The Quarterly Journal of Mathematics
(2020), pdf.
- Enumerating graded ideals in graded rings associated to free nilpotent
Lie rings, with S. Lee, Math. Z. 290 (2018),
1249--1276, pdf, arxiv
- Enumerating traceless matrices over compact discrete valuation rings,
with A. Carnevale and S. Shechter, Israel J. Math. 227 (2018),
956--986, pdf, arxiv
- Orbit Dirichlet series and multiset permutations, with A. Carnevale,
Monatsh. Math. 186 (2018),
215--233, pdf, arxiv
- Local functional equations for submodule zeta functions associated to
nilpotent algebras of endomorphisms, Int. Math. Res. Not. IMRN
(2017), pdf, arxiv
- Representation zeta functions of some nilpotent groups associated to
prehomogenous vector spaces, with A. Stasinski, Forum Math. 29 (2017),
717--734, pdf, arxiv,
- 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,
- 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
- 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.
- Enumerating classes and characters of p-groups, with
E. A. O'Brien, Trans. Amer. Math. Soc. 367 (2015), 7775 --
7796, pdf, arxiv
- 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
- 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
- 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
- A New Statistic on the Hyperoctahedral Groups, with
A. Stasinski, Electron. J. Combin. 20, issue 3 (2013),
P50, pdf, arxiv
- 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
- 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
- Functional equations for zeta functions of groups and rings,
Ann. Math. 172 (2010),
1181--1218, pdf, arxiv
- 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
- Enumerating finite class-2-nilpotent groups on 2 generators,
C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 1347-1350, pdf, arxiv
- Zeta function of 3-dimensional p-adic Lie algebras, with
B. Klopsch, Math. Z. 263, No. 1 (2009),
195--210, pdf, arxiv
- 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
- 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
- Counting subgroups in a family of nilpotent semidirect
products, Bull. London Math. Soc., No. 38 (2006),
743--752, pdf, arxiv
- Normal subgroup growth in free class-2-nilpotent groups,
Math. Ann. 332, No. 1 (2005), 67--79,
pdf, arxiv
- 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
- Zeta functions of groups and enumeration in Bruhat-Tits
buildings, Amer. J. Math. 126 (2004),
1005--1032, pdf, arxiv
Selected grants
- 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.
Meetings (co-)organised
- with B. Klopsch, W. Veys, W. Zuniga-Galindo,
week-long Fourth
International Workshop on Zeta Functions in Algebra and Geometry,
Bielefeld, 29 May - 02 June 2017
- with E. Detomi, B. Klopsch, A. Lucchini, four-day workshop
on Zeta functions
of groups and related algebraic structures, 22-25 September 2013
in Padova
- with B. Klopsch, two-day workshop
on Asymptotic Group
Theory and Model Theory, 26-27 March 2012 at Royal Holloway
University of London
- with B. Klopsch, two-day workshop
on Representations
and Asymptotic Group Theory, 6-7 April 2009 in Southampton
- with N. Avni and U. Onn, I was involved in the organisation of
the Batsheva
seminar on Representation Growth, 21-26 June 2009 in Sde-Boker,
Israel
- From 2007 until 2013 I was involved in
the South
England Profinite Groups Meetings, a Joint Research Group
supported by an LMS Scheme 3
grant
Postdocs
- Viola Siconolfi, 2022 - present
- Seungjai Lee, 2019 -
present
- Josh Maglione, 2018 - present, funded partyly by DFG
- Mima
Stanojkovski, 2017 - present (currently MPI MIS, Leipzig (Sturmfels group))
- Alastair
Litterick, 2016 - 2019, Alexander von Humboldt-Fellow, now Lecturer at the University of Sussex, UK.
- Thomas Cauwbergs,
2015 - 2017, funded
by DFG Sonderforschungsbereich
701
- Angela
Carnevale, 2015 - 2018, partly funded
by German-Israeli
Foundation, now Lecturer at the National University of Ireland Galway
- Ann Kiefer,
2015 - 2017, FWO Postdoctoral Fellow, now postdoc at the Vrije
Universiteit Brussel
- Matthew Levy, 2014 - 2016
- Tobias
Roßmann, 2011 - 2016, funded
by DFG Priority
Programme "Algorithmic and Experimental Methods in Algebra,
Geometry, and Number Theory" 1489, now Lecturer at the National University of Ireland Galway
- Duong Hoang
Dung, 2013 - 2015, funded by
DFG Sonderforschungsbereich
701, now Lecturer at the University of Wollongong, Australia
- Alexander
Stasinski, 2009 - 2011, funded
by EPSRC First
Grant EP/F044194/1, now Associate Professor at the University of Durham
PhD students
- Marlies Vantomme, 2019 - present
- Elena Tielker, 2018 - present, funded by DFG
- Paula Lins, 2015 - 2018 (degree awarded January 2019), now postdoc at KU Leuven Kulak, Belgium
- Michele Zordan, 2010 - 2015 (degree
awarded April 2016), now Research Assistant at Imperial College, London
- Robert Snocken, 2008 - 2012 (degree awarded December 2014)
Teaching (in German)
Sommersemester 2020
Wintersemester 2019/20
Sommersemester 2019
Forschungsfreisemester (sabbatical)
Wintersemester 2018/19
- Algebra 1
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Sommersemester 2018
Wintersemester 2017/18
Sommersemester 2017
- Mastervorlesung Lie Algebras and Lie Groups (je nach Bedarf auf
Englisch oder Deutsch)
- Proseminar Graphentheorie
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Wintersemester 2016/17
Sommersemester 2016
Wintersemester 2015/16
- Vorlesung Lineare Algebra für Physik
- Bachelorseminar "Die symmetrische Gruppe - Algebra und Kombinatorik"
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Sommersemester 2015
- Vorlesung Algebra 2
- Proseminar Coxetergruppen
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Wintersemester 2014/15
- Vorlesung Algebra 1
- Seminar Local Cohomology (with H. Krause, in English)
- Proseminar Graphentheorie
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Sommersemester 2014
Forschungsfreisemester (sabbatical)
Wintersemester 2013/14
Sommersemester 2013
Wintersemester 2012/13
- Vorlesung Lineare Algebra 2
- Proseminar Lineare Algebra
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Sommersemester 2012
- Blockvorlesung "An Introduction to Lie groups and Lie algebras"
von Dr. Uri
Onn vom 16. - 27. Juli 2012. Teilfinanziert durch
dasGastdozentenprogramm der Universität Bielefeld.
- Vorlesung Lineare Algebra 1
- Seminar Kommutative Algebra und Kombinatorik
- (Didaktik-)Seminar / Bachelorarbeit Gruppentheorie
- Arbeitsgemeinschaft Asymptotische Gruppentheorie
Wintersemester 2011/12
- GHR-Vertiefungsvorlesung Gruppen und Symmetrie
- Vorlesung Kommutative Algebra
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Last updated: 24 June 2020