Fathi Ben Aribi     Version en français

FathiBenAribi

Contact :

Campus Pierre et Marie Curie (Jussieu)
4 place Jussieu,
Boite Courrier 247
75252 Paris Cedex 5
France

Office : 16-26-529
Phone number: +33 (0)144272702
Email: benaribi(at)imj-prg(dot)fr

Since September 2023, I am a Maître de Conférences (which might be called "Associate Professor" in English, but I'm not sure!) in Sorbonne-Université; my research takes place in the Institut de Mathématiques de Jussieu - Paris Rive Gauche, in the team Analyse Complexe et Géométrie, and I teach at the INSPE Paris.
Until August 2023, I was a Scientific collaborator (postdoc) at the Université catholique de Louvain, in the team of Pedro Vaz.
Previously I was a Chargé de Recherches FNRS in the same team, and before this i was a postdoc in the University of Geneva.

Research Interests:

My research domain is Geometric Topology, and most of my research works are in Knot Theory. More precisely, here are some of my interests:
I am especially interested in connections between these domains, such as the ones between the L2-Alexander invariant of knots (an infinite-dimensional version of the Alexander polynomial I studied during my PhD) or the Teichmüller TQFT (a quantum invariant of triangulated 3-manifolds I studied after my PhD) with the hyperbolic volume.

I am also part of the SyTriQ ANR Project (Trisections and symplectic structures on smooth 4-manifolds & Higher dimensional generalizations) led by Delphine Moussard, for the time period 2020-2024.

Preprints:

  1. FAMED by computer: proving the Andersen-Kashaev volume conjecture for 42,000 knots (with A. Guilloux and K.H. Wong),
    2. 14 pages, arXiv 2512.17437 (december 2025).

  2. The Andersen-Kashaev volume conjecture for FAMED geometric triangulations (with K.H. Wong),
    3. 45 pages, arXiv 2410.10776 (october 2024).

  3. Multisections of higher-dimensional manifolds (with S. Courte, M. Golla and D. Moussard),
    4. 14 pages, arXiv 2303.08779 (march 2023).

  4. The Chen-Yang volume conjecture for knots in handlebodies (with J. Gosselet),
    5. 34 pages, arXiv 2110.04225 (october 2021).

  5. Link invariants from L2-Burau maps of braids,
    6. 24 pages, arXiv 2101.01678v4 (july 2021).

Publications:

  1. Computing the topological volume of some three-manifolds, (with B. Burton, D. Ibarra, J. Morgan, J. Purcell, J. P. Quintanilha, D. Santoro, S. Schleimer, and E. Thompson),
    2. Oberwolfach Rep. 21, No. 3, 2530-2535 (2024).

  2. Fuglede-Kadison determinants over free groups and Lehmer's constants
    3. Confluentes Mathematici, 214, 1 (2022) 3--22. [ArXiv] (february 2022).

  3. Geometric triangulations and the Teichmüller TQFT volume conjecture for twist knots (with F. Guéritaud and E. Piguet-Nakazawa),
    4. Quantum Topology, 14 (2023), no. 2, pp. 285-406. [ArXiv] (february 2020).

  4. The leading coefficient of the L2-Alexander torsion (with S. Friedl and G. Herrmann),
    5. Annales de l'Institut Fourier, Tome 72 (2022) no. 5, pp. 1993-2035. [ArXiv] (june 2018).

  5. The Teichmüller TQFT Volume Conjecture for twist knots (with E. Piguet-Nakazawa),
    6. C. R. Math. Acad. Sci. Paris 357, 2019, no. 3, 299-305. [ArXiv] (october 2018)

  6. L2-Burau maps and L2-Alexander torsions (with A. Conway),
    7. Osaka J. Math. 55 (2018), 529-545. [ArXiv] (august 2016).

  7. The L2-Alexander invariant is stronger than the genus and the simplicial volume,
    8. Journal of Knot Theory and Ramifications Vol.28, No.05, 1950030, 2019, 16 pages. [ArXiv] (june 2016).

  8. Gluing formulas for the L2-Alexander torsions,
    9. Communications in Contemporary Mathematics 1850013, 2018, 31 pages, World Scientific Publishing Company, DOI:10.1142/S021919971850013X. [ArXiv] (march 2016).

  9. The L2-Alexander invariant detects the unknot,
    10. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XV (mars 2016), 683-708. [ArXiv] (november 2013).

  10. The L2-Alexander invariant detects the unknot,
    11. C. R. Math. Acad. Sci. Paris 351, 2013, no. 5-6, pages 215-219 (march 2013).

My PhD thesis:

My thesis is called "A study of properties and computation techniques of the L2-Alexander invariant in knot theory" and was done under the supervision of Jérôme Dubois. My defense was the 10th July 2015 at the Université Paris 7.

Recent invitations to international conferences:

Slides from recent talks:

Thesis supervision:

In 2020-2021, at the UCLouvain, I co-supervised (with Pedro Vaz) the Master's thesis of James Gosselet, entitled " The Chen-Yang volume conjecture for knots in handlebodies".

Lecture Notes:

Advice for preparing Math talks:

In 2018 I did a survey of various types of advice for preparing and/or giving talks in mathematical research, and I summarised them in one big list of 50 tips. I hope this can be useful to you or someone you know!

Fictions for scientific outreach:

Scientific Outreach (in French):