Home Page of
François Costantino
Publications . Conferences . Enseignement . Students . Videos

Full Professor at
Institut de Mathématique de Toulouse (IMT)
Université Toulouse III Paul Sabatier
118 route de Narbonne - F-31062 TOULOUSE Cedex 9 (France)
Tel: 0033   Fax: 0033
e-mail: Francesco.Costantino(at)math.univ-toulouse.fr

Research Interests: Geometry and Topology of low-dimensional manifolds, Topological Quantum Field Theories (TQFTs) and their relations to geometry.


Papers . Memoirs


  1. Skein (3+1)-TQFTs from non-semisimple ribbon categories (with B. Haioun, N.Geer and B.Patureau) arXiv:2306.03225 .

  2. Chromatic maps for tensor categories (with N.Geer, B.Patureau and A.Virelizier) arXiv:2305.14626.

  3. Non compact (2+1)-TQFTs from non-semisimple spherical categories (with N.Geer, B.Patureau and A.Virelizier) arXiv:2302.04509.

  4. Admissible Skein Modules (with N.Geer and B.Patureau) arXiv:2302.04493.

  5. Stated skein modules of 3-manifolds and TQFT (with T.Le) arXiv:2206.10906.

  6. Nonsemisimple TQFT's and BPS $q$-series (with S.Gukov and P.Putrov) . https://arxiv.org/abs/2107.14238 to appear on SIGMA

  7. Stated skein algebras of surfaces (with T.Q. Le). In publication on Journal of the European Mathematical Society (2020) . https://arxiv.org/abs/1907.11400

  8. Kuperberg and Turaev-Viro invariants in unimodular categories, (with N.Geer, B. Patureau-Mirand and V. Turaev). https://arxiv.org/abs/1809.07991, in publication to Pacific Journal of Mathematics.

  9. Non-semi-simple TQFTs, Reidemeister torsion and Kashaev’s invariants (With Christian Blanchet, Nathan Geer and Bertrand Patureau), Adv. Math. 301 (2016).

  10. Duality between Spin networks and the 2D Ising model. (With Valentin Bonzom and Etera Livine) Communications in Mathematical Physics (2016), available on ArXiv: arXiv:1504.02822 (2015)

  11. Non semi-simple TQFTs from unrolled quantum sl(2). (With Christian Blanchet, Nathan Geer and Bertrand Patureau), Proceedings of the Gökova Geometry and Topology Conference 2015.

  12. Notes on Topological Quantum Field Theories. Notes of a course I gave at Winter Braids 2015. Published in Winter Braids Lecture Notes, 2 : Winter Braids V (Pau 2015) (2015), Exp. No.1.

  13. Generating series and asymptotics of classical spin networks. (With Julien Marché)
    Journal of The European Mathematical Society (JEMS), vol 17, Issue 10 (2015) . Available on ArXiv:

  14. Relations between Witten-Reshetikhin-Turaev and non semi-simple sl(2) 3-manifold invariants. (With Nathan Geer and Bertrand Patureau)
    Algebraic Geometry and Topology, 15 (2015) 1363-1386. Available on ArXiv:

  15. Some remarks on the unrolled quantum group of sl(2). (With Nathan Geer and Bertrand Patureau)
    Journal of Pure and Applied Algebra 219 (8), pp. 3238-3262 (2015). Available on ArXiv:

  16. On the volume conjecture for polyhedra. (With François Guéritaud and Roland van der Veen)
    Geometriae Dedicata, vol. 179, Issue 1 (2015), pp 385-409. Available on ArXiv:

  17. An analytic family of representations for the mapping class group of punctured surfaces. (With Bruno Martelli) Geometry & Topology 18 (2014), 1485-1538. Available on ArXiv: arXiv:1210.2666

  18. Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories. (With Nathan Geer and Bertrand Patureau) Journal of Topology (2014) . Also available on ArXiv: arXiv:1202.3553. The published version contains a mistake in the proof of Theorem 4.10. The appendix to the following version contains an erratum correcting this.

  19. Non semi-simple sl(2) quantum invariants, spin case. (With Christian Blanchet, Nathan Geer and Bertrand Patureau) Acta Mathematica Vietnamica, vol. 39, Issue 14 (2014) pp. 481-495. Available on ArXiv: arXiv:1405.3490

  20. Integrality of Kauffman brackets of trivalent graphs. Quantum Topology. Volume 5, Issue 2 (2014), 143-184. Also Available on ArXiv: arXiv:0908.0542

  21. On the SL(2, C) quantum 6j-symbols and their relation to the hyperbolic volume. (With Jun Murakami)
    Quantum Topology Vol. 4, Issue 3 (2013), pp. 303-351. Also Available on ArXiv:

  22. 6j-symbols, hyperbolic structures and the Volume Conjecture. Geometry Topology 11 (2007), 1831-1853 . Also Available on ArXiv: http://arxiv.org/abs/math/0611399

  23. 3-manifolds efficiently bound 4-manifolds. (With Dylan Thurston) Journal of Topology vol. 1, n. 3, (2008) . Also available on ArXiv: http://arxiv.org/abs/math/0506577

  24. Triangulations of 3-manifolds, hyperbolic relative handlebodies, and Dehn filling. (With Roberto Frigerio, Bruno Martelli and Carlo Petronio) Commentarii Mathematici Helvetici Volume 82, Issue 4, 2007, pp. 903-933. Also available on ArXiv: http://arxiv.org/abs/math/0402339

  25. Colored Jones invariants of links in S^3 # k S^2 X S^1 and the Volume Conjecture.
    J. Lond. Math. Soc. 76 (2007), no 1, 1-15 . Also Available on ArXiv:

  26. Stein domains and branched shadows of 4-manifolds. Geometriae Dedicata (2006), vol 121, issue 1, 89-111 . Also Available on ArXiv: http://arxiv.org/abs/math/0504387

  27. Complexity of 4-manifolds. Experimental Mathematics 15, No 2 (2006), 237-249.

  28. Branched shadows and complex structures of 4-manifolds. Journal of Knot Theory and its Ramifications 17 (2008) no 11, 1429-1454 . Also available on ArXiv: http://arxiv.org/abs/math/0502292

  29. A calculus for branched spines of 3-manifolds. Mathematische Zeitschrift (2005), Volume 251, Issue 2, pp 427-442. Also available on ArXiv: http://arxiv.org/abs/math/0403014

  30. Euler structures and Reidemeister torsion of three manifolds. (With Riccardo Benedetti, Carlo Petronio and Gennaro Amendola) Rendiconti dell'Istituto Matematico dell'Università di Trieste, Supp. Vol. XXXII pp. 1-23 (2001)..

  31. On a proof of the JSJ Theorem. Rendiconti del Seminario Matematico dell'Università e del Politecnico di Torino,vol. 60 n. 3 (2002).

My "Memoire d'Habilitation à Diriger des Recherches" and my Ph.D. Thesis

Réseaux de spin et leur géométrie (.pdf file)
Mémoir of my "Habilitation à Diriger des Recherches" defended at IRMA the 17th of October 2011.
Jury: Norbert A'Campo (Président), Christian Blanchet, Michel Boileau, Vladimir Fock, Christian Kassel, Vladimir Turaev .

Shadows and branched shadows of 3 and 4-manifolds
PhD. Thesis defended at Scuola Normale Superiore di Pisa the 24th of Mai 2004.
Jury: Giuseppe Tomassini (Président), Riccardo Benedetti (advisor), Paolo Lisca, Wolfgang Metzler, Bernard Perron, Carlo Petronio, Mario Salvetti, Bruno Zimmermann.
The thesis was later published by the Edizioni della Scuola Normale Superiore di Pisa.


Organized Conferences


Notes de Cours

My (former) students


Last modified: June the 19th 2023