About Me

I am a postdoctoral fellow of the FWO and FNRS. This year I am working in the research groups of Pedro Vaz at UCLouvain and of Kenny De Commer at the Free University of Brussels. I obtained my PhD there on the 19th of May 2017 under the supervision of Eric Jespers (Brussels, VUB) and Alexey Gordienko (Moscow, MSTUCA). Currently, I am visiting Bernhard Keller at l'université Paris cité.

  • You can download my CV here (last updated on 22/02/2023)

You can find me here:

Vrije Universiteit Brussel
Departement wiskunde
Pleinlaan 2
1050 Brussels

Office: 6G322b

Don't hesitate to jump by or to contact me by email: geoffrey.janssens@vub.be


  • My bachelor student Robynn Corveleyn presented on 29th of january 2021 with conviction and aesthetically her work (on expliticising and optimizing the algorithm behind the proof of a theorem of Wilson-Zelmanov which translates a law on a group into a polynomial identity of the associated Lie algebra via Lazard's construction). Proficiat!
  • Happy that Doryan Temmerman will be able to continue his algebraic journey with a post-doc at the University of Hasselt.
  • On 31st of january 2020 my two bachelor students, Julie Symons and Maxime Wybouw, defended passionately their work (on a paper of S. Eberhard on commuting probabilities, respectively on the (classical) Schur-Weyl duality). Nice to see such a passion grow! Looking forward to see their next mathematical steps!
  • On 24th of May 2019 Doryan Temmerman, my first mathematical son, defended his Ph.D with glance and originality! Congratz!!
  • We are organising a conference "Groups, Rings and associated structures" in Spa, Belgium, June 09-15, 2019.

Research interests

My research lies in representation theory, interpreted broadly, both of finite groups and any algebras. Currently, I especially enjoy thinking about the connections between additive and monoidal categorifications of cluster algebras arising from Lie theory. In particular I am interested on anything touching Quantum Affine Algebras. The last 6 years I have also been investigating integral representations of finite groups. Hereby my point of view has rather been one of a geometric group theorist. More precisely questions centered around which properties of a finite group G is encoded in the unit group of its integral group ring, considered as an arithmetic group in an appropriate semisimple algebraic group, captured my attention. Before that, in the first years of my phd, I studied some combinatorial invariants associated to any PI algebra (where representation theory of the symmetric group was a close friend).


  1. Units of twisted group rings and their correlations to classical group rings,
    joint with E. Jespers and Ofir Schnabel
    arXiv | ▸ Abstract
  2. Glider Representation Rings with a view on distinguishing groups, 2019, 34 pages
    joint with F. Caenepeel
    arXiv | ▸ Abstract

Published or accepted papers

  1. Higher modular groups as amalgamated products and a dichotomy for integral group rings, J. Algebra 604 (2022), 185–223
    joint with A. Bächle, E. Jespers, A. Kiefer and D. Temmerman
    arXiv | ▸ Abstract
  2. Codimension Growth of Lie algebras with a generalized action, 2021, Proc. Amer. Math. Soc. , 150 (2022), no. 7, 2741–2754
    arXiv | ▸ Abstract
  3. Abelianization and fixed point properties of linear groups and units in integral group rings, Math. Nachr. , 296 (2023), no. 1, 8–56
    joint with A. Bächle, E. Jespers, A. Kiefer and D. Temmerman
    arXiv | ▸ Abstract
  4. A glimpse into the Asymptotics of polynomial identities, Nieuw Arch. Wiskd. (5) 18 (2017), no. 1, 60-64
    Journal | ▸ Abstract
  5. Free products in the unit group of the integral group ring of a finite group, Proc. Amer. Math. Soc. 145 (2017), no. 7, 2771-2783
    joint with E. Jespers and D. Temmerman
    arXiv | Journal | ▸ Abstract
  6. A reduction theorem for $\tau$-rigid modules, Math. Z. (2018), 1-37
    joint with F. Eisele and T. Raedschelders
    arXiv | Journal (open access) | GAP-code | ▸ Abstract
  7. The Polynomial Part of the Codimension Growth of Affine PI algebras, Adv. Math. 309 (2017), 487-511.
    joint with E.Aljadeff and Y.Karasik
    arXiv | Journal | ▸ Abstract
  8. Semigroup graded algebras and graded PI-exponent, Israel J. Math. 220 (2017), no. 1, 387-452.
    joint with A.Gordienko and E. Jespers
    arXiv | Journal | ▸ Abstract
  9. $\mathbb{Z}$Sn-modules and polynomial identities with integer coefficients, Int. J. Algebra Comput. 23 (2013), no. 8, 1925-1943.
    joint with A.Gordienko
    arXiv | Journal | ▸ Abstract
  10. Primitive Central Idempotents of Rational Group Algebras, J. Algebra Appl. 12 (2013), no. 1, 125-130.
    arXiv | Journal | ▸ Abstract
My arXiv profile can be found here and my Google Scholar profile is here .

  • Identities of Affine Algebras and their Asymptotic Behaviour
    Ph.D thesis
    CCC Productions, 2017, 201 pp, ISBN: 9789492312396
    download (pdf)
  • The Isomorphism Problem for Integral Group Rings of Finite Groups
    Master Thesis
    Vrije Universiteit Brussel, 2012
    download (pdf)
  • A Glimpse into the asymptotics of Polynomial identities
    Conference Groups, Rings and the Yang-Baxter equation, Spa, Belgium, June 20, 2017
    download (pdf)
  • A reduction theorem for Tau-Rigid Modules
    ICRA, Syracuse university, US, August 15, 2016
    download (pdf)
  • Identities of Algebras and Group and their Asymptotic behaviour
    BeNeLux conference, Univ. of Amsterdam, Netherlands, March 23, 2016
    download (pdf)
  • PI-exponent and Structure of Lie algebra with an Algebra acting
    Conference, Bulgarian Academy of Sciences, Sofia, July 16, 2015
    download (pdf)
  • ZS_n-modules and polynomial identities with integer coëfficients
    Conference, Brock University, Canada, July 29, 2014
    download (pdf)
  • Primitive central idempotens of rational group algebras
    Conference, Canada, August 17, 2013
    download (pdf)

Ring- en Moduultheorie

  • Laatste versie (15-11-19) van de syllabus: zie hier.
  • Theorie lessen: di 13-16u in F5.203 (week 14) & wo 10-12u in K2.auditorium 4 (weken 4-5,7,9,11-13) en in F5.204 (weken 3,8)
  • Oefeningen lessen: wo 10-12u in K2.auditorium 4 (weken 6,14) & do 15-17u
  • De presentaties vinden plaats op dinsdag 18 december van 13-16u!
  • Het examen: 20-01 om 13u in lokaal E0.05 om (theorie) & 20-01 om 9u in lokaal D2.16 (oefeningen)

Lineaire algebra: stelsels, matrices en afbeeldingen

WPO Lineaire Algebra 2013 - 2014

1st Bachelor Chemistry and Computer sciences + verkort proramma Computer Sciences

WPO Lineaire Algebra 2012 - 2013

1st Bachelor Computer sciences + verkort proramma Computer Sciences

“If you have an apple and I have an apple and we exchange these apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas.” G.B. Shaw

The quote above is a famous one, but nevertheless I truly find the process of collaboration fascinating and invaluable and so I fully adhere to Shaw's view. Another famous quote, that complements, is one of Hilbert: "Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country". I was especially glad to discover that my 'mathematics genealogy' reflects this (enjoy going through math history! :))

Co-authors and Current Collaborators:

Israel Institut of Technology

Eli Aljadeff

Vrije Universiteit Brussel

Andreas Bächle

Fundan University

Frederik Caenepeel

Moscow State Technical University of Civil Aviation

Alexey Gordienko

City, University of London

Florian Eisele

Vrije Universiteit Brussel

Eric Jespers

University of Ljubljana

Urban Jezernik

Université de Paris - Paris 7 Diderot

Bernhard Keller

University of Luxembourg

Ann Kiefer

Justus-Liebig-Univeristät Giessen

Yaakov Karasik

Vrije Universiteit Brussel

Theo Raedschelders

ORT Braude College

Ofir Schnabel

Universiteit Hasselt

Doryan Temmerman