Jules Martel
Contact :
Université de Cergy-Pontoise,
Site de Saint-Martin,
2 avenue Adolphe Chauvin,
95300 Pontoise, France.
Email: Jules.Martel-Tordjman(at)cyu(dot)fr
I am currently a postdoc (non-permanent enseignant--chercheur contractuel) at Cergy Paris University. I am on the job market, please contact me for my application material.
Research Interests
My field of research is low dimensional topology, more precisely knots, braids, mapping class groups, manifolds etc, interplaying with representation theory (e.g. of Hopf algebras).
On one hand I study quantum topology, namely topological invariants arising from quantized Lie algebras such as knot invariants, braid representations, quantum representations of mapping class groups.
On the other hand, I'm interested in homology of configuration spaces, related homology techniques in the context of local coefficients.
I have defended my PhD in December 2019, under the supervision of Professor F. Costantino, at Université Paul Sabatier, Toulouse 3. It is entitled ``Homological interpretations for quantum invariants''.
Then I was a postdoc fellow at the Max Planck Institute for Mathematics, Bonn, and then at the Institut de mathématiques de Bourgogne, in Dijon, France, and then at the University of Zürich, Swiss.
Accepted paper
- J. Martel, A homological model for Uq sl(2) Verma-modules and their braid representations ArXiv (February 2020), Geometry & Topology 26-3 (2022), 1225--1289. DOI 10.2140/gt.2022.26.1225.
- J. Martel, The non semi-simple TQFT of the sphere with four punctures ArXiv (June 2020), Jounral of knot theory and its ramifications Volume 30, Issue 06 (May 2021).
- J. Martel, Colored version for Lawrence representations, to appear at NYJ Maths , ArXiv preprint (April 2020).
- J. Martel, Colored Jones polynomials and abelianized Lefschetz numbers, ArXiv preprint, Advances in Maths Volume 438, February 2024, 109453.
- J. Martel, S. Willetts, Unified invariant of knots from homological braid action on Verma modules, ArXiv preprint, to appear at Proceedings of the London Maths Society .
Preprints
- M. De Renzi, J. Martel, Homological Construction of Quantum Representations of Mapping Class Groups, submitted, ArXiv preprint (December 2022).
- M. De Renzi, J. Martel, B. Wang, Hennings TQFTs for cobordisms decorated with cohomology classes, submitted, ArXiv preprint (Feb. 2024).
PhD thesis
My thesis is called "Homological interpretations for quantum invariants", supervised by F. Costantino. You can read the manuscript (not yet on HAL for covid reasons) .
Organisation
- I (co)-organized the following weekly seminar: Mapping class groups of surfaces: different aspects . It happens every tuesday in Dijon (France) for the year 2021-2022.
- I (co)-organize the annual conference Topology Between The Waves:
- First edition: BTW I: Homological and quantum invariants , at the CIRM in Marseille (France), February 2021.
- Second edition: BTW II: Sliceness, Exotic pairs and Quantum invariants , in Aussois (France), April 2022.
- Third edition: BTW III: Morse and Floer Theories , at the CIRM in Marseille (France), January 2023.
- Fourth edition: BTW IV: Knot Floer Homology , at the Station biologique du CNRS, Besse (France), Feb. 2024.
Talks (Videos)
You may find talks I gave in videos following the links:
J. Martel, A full homological model for quantum Verma modules and their representations of braid groups., [K-OS] seminar, 30/04/2020.
J. Martel, Braid representations and Kohno's theorem (I) and (II)., Matemale winter school, April 2018, talk (I), and talk (II).
And a talk for psychoanalysts who want to learn about topology and knots (in french) :
J. Martel, J.-M. Valtat, Une clinique de l'angoisse à partir de la mathématiques des noeuds., Ecole de Psychanalyse du Forum des Champs Lacaniens, Paris, 29/03/2024.
A little bit of epidemiology
Tô Tat Dat, Protin Frédéric, Nguyen T.T. Hang, Martel Jules, Nguyen Duc Thang, Charles Piffault, Rodríguez Willy, Figueroa Susely, Hông Vân Lê, Wilderich Tuschmann, Nguyen Tien Zung, Epidemic Dynamics via Wavelet Theory and Machine Learning, with Applications to Covid-19, ArXiv preprint (October 2020), accepted in Biology.
F. Protin, J. Martel, D.T. Nguyen, H. T.T. Nguyen, C. Piffault, W. Rodríguez, S. Figueroa, Tat Dat Tô, W. Tuschmann, Hông Vân Lê, T. Yeo, Tien Zung Nguyen Unified modelling of epidemics by coupled dynamics via Monte-Carlo Markov Chain algorithms, ArXiv preprint (June 2021).