Ce groupe de travail, désormais à sa 5eme séance, a comme but d’explorer les liens entre différentes constructions de la topologie quantique à savoir :

• Algèbres skein et stated skein
• Moduli algebra
• TQFTs
• Homologies des espaces de configuration de points
• Homologie de factorisation

Le groupe de travail est ouvert à tous les collègues intéressés. L’inscription n’est pas obligatoire.

Nous remercions la Fédération Occimath ainsi que l’Institut Montpelliérain de Mathématiques qui soutiennent ce groupe de travail.

Programme :

Mardi 26 mai, 14h00 : Exposé par David Jordan (Edinburgh) « Holonomicity for skein modules ». Résumé: In this talk I will explain our recent proof with Iordanis Romaidis that the skein module of an oriented 3-manifold with boundary is finitely generated and holonomic over the skein module of the boundary.  This proves a conjecture of Detcherry, gives a new proof of holonomicity of the coloured Jones polynomial (first proved by Garoufalidis and Le) and also establishes the non-triviality of the annihilator of the empty skein (as conjectured by Frohman,  Gelca and Lofaro).

Mardi 26 mai, 15h30 : Exposé par Matt Young (Utah State University) « Topological field theories from quantum Lie superalgebras ». Résumé: The goal of this talk is to explain ongoing work aimed at understanding three-dimensional non-semisimple topological field theories (TFTs) constructed from quantizations of Lie superalgebras. First, I will describe recent joint work with S. Porter that constructs such theories from orthosymplectic Lie superalgebras of type C in Kac’s classification. Combined with the work of many others, this yields a construction of TFTs from each basic classical Lie superalgebra of type I (at suitable roots of unity). Second, I will survey some connections between these TFTs and 3-manifold invariants appearing in the physics literature, namely the Rozansky–Witten and Z-hat invariants.

Mercredi 27 mai, 9h30 : Exposé par Matthieu Faitg (IMT Toulouse) « On deformation of module categories ». Résumé: A module category is a category equipped with an action of a monoidal category and a natural isomorphism, called « mixed associator », which controls the associativity of the action. In this talk I will define a cohomology theory for deforming such a mixed associator. The main result is that this cohomology is related to certain « relative Ext groups », and can thus be explicitly computed using « relative projective resolutions ». These are notions from relative homological algebra which I will explain.
Joint work with A. Gainutdinov and C. Schweigert (arXiv:2604.00837).