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

Publications

1. Learning 3-manifold triangulations (with Y.H. He, E.Hirst and E. Heyes). arXiv:2405.09610 .  


2. Fisher-Rao distance between truncated distributions and robustness analysis in uncertainty quantification (with B.B. Ketema, N. Bousquet, F.Gamboa B. Ioos and R. Sueur). arXiv:2405.21542 .  


3. Non-semisimple topological field theory and Z-invariants from osp(1|2) (with M. Harper, A. Robertson, M. B. Young). arXiv:2405.12181 .  


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


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


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


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


8. Stated skein modules of 3-manifolds and TQFT (with T.Le) arXiv:2206.10906. Accepted for publication on Journal of the Institut de Mathématiques de Jussieu.


9. Nonsemisimple TQFT's and BPS $q$-series (with S.Gukov and P.Putrov) . SIGMA 19 (2023), 010, 71 pages.


10. Stated skein algebras of surfaces (with T.Q. Le). J. Eur. Math. Soc. 24 (2022), no. 12, pp. 4063�4142. https://arxiv.org/abs/1907.11400


11. Kuperberg and Turaev-Viro invariants in unimodular categories, (with N.Geer, B. Patureau-Mirand and V. Turaev). https://arxiv.org/abs/1809.07991, Pacific J. Math. 306 (2020) 421-450.


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


13. 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)


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


15. 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.
    


16. Generating series and asymptotics of classical spin networks. (With Julien March�)
    Journal of The European Mathematical Society (JEMS), vol 17, Issue 10 (2015) . Available on ArXiv: arXiv:1103.5664


17. 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: arXiv:1310.2725


18. 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: arXiv:1406.0410


19. On the volume conjecture for polyhedra. (With Fran�ois Gu�ritaud and Roland van der Veen)
    Geometriae Dedicata, vol. 179, Issue 1 (2015), pp 385-409. Available on ArXiv: arXiv:1403.2347


20. 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


21. 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.


22. 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


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


24. 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: arXiv:1005.4277


25. 6j-symbols, hyperbolic structures and the Volume Conjecture. Geometry Topology 11 (2007), 1831-1853 . Also Available on ArXiv: http://arxiv.org/abs/math/0611399


26. 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


27. 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


28. 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: http://arxiv.org/abs/math/0510048


29. 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


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


31. 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


32. An introduction to shadows of 4-manifolds. Fund. Math.,Volume: 188, Issue: 1, page 271-291 (2005). .


33. 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


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


35. On a proof of the JSJ Theorem. Rendiconti del Seminario Matematico dell'Universit� 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) Memoire of my "Habilitation à Diriger des Recherches" defended at IRMA the 17th of October 2011. Jury: Norbert A'Campo (President), 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 (President), 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.

Conferences

Organized Conferences

• In july 2023 I co-organised the special session of the conference Nordic Congress of Mathematicians (NCM29) in Aalborg on Quantum Chern-Simons theory (Denmark) Paris.
• In june 2022 I co-organised the conference Quantum topology and geometry in honor of Vladimir Turaev at IHP Paris.
• In september 2021 I organised a one day conference on "IA, geometry and topology" at IMT in the framework of TOUTELIA conferences.
• In fall 2019 I coorganised the CIMI thematic semester Statistics with Geometry and Topology at IMT.
• In february 2019 I coorganised (with B Leclerc and H. Queffelec) the conference ``Categorification in topology and representation theory'', Caen 
• In spring 2017 I organized (together with J. Aramayona, T. Fiedler, P. Haissinsky and C. Lecuire) a semester of activities on "Invariants in low dimensional geometry and topology". 
• Mapping Class Groups and Quantum Topology, 25-29 June 2012, IRMA Strasbourg.
  Organizers : Francesco Costantino, Jérome Dubois, Gwénael Massuyeau.
• Quantum Geometry and Topology , 5-9 July 2010, CIRM Luminy.
  Organizers : Stéphane Baséilhac, Francesco Costantino, Jérome Dubois, Julien March�.
• Journée Géométrie, Topologie et Physique : Invariants par somme d'état des 3 et 4 variétés, February the 28th 2008, IRMA Strasbourg.
  Organizer: Francesco Costantino.
• Journ�e Géométrie, Topologie et Physique : Gravité quantique / Loop Quantum Gravity, December the 6th 2007, IRMA Strasbourg.
  Organizer: Francesco Costantino.
• Journées ANR sur la Conjecture du Volume , 17-19 September 2007, IRMA Strasbourg.
  Organizers : Stéphane Baséilhac, Francesco Costantino, Gwénael Massuyeau.