Journées de topologie quantique

The “journées de topologie quantique” (quantum topology days) are a regular event aiming at bringing together, in a somewhat informal setting, people thinking about quantum topology in a broad sense. As the name suggests this is a one day event, with three talks and lots of time for discussions, taking place either in Paris or in Dijon.

Next session: 18 March 2023


Registration is free but mandatory. Please fill the following form:

Location: Paris

Amphi Turing, bâtiment Sophie Germain


Quantum moduli algebras are a quantization of character varieties of surfaces which have been introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the 90's. I will explain the definition of these algebras (based on quantum groups) and give structure results, namely they are finitely generated, Noetherian and do not have zero divisors. Then I will relate quantum moduli algebras with skein algebras, which is one the motivation for these results. I will finish by a few words on the specialization of quantum moduli algebras at roots of unity. Joint work with S. Baseilhac and P. Roche.

I will recall some tools from non-semisimple skein theory. The key players are modfied traces, which were introduced to obtain invariants of links with a projective strand for which the usual Reshetikhin–Turaev theory gives trivial invariants. I will explain how they give the first step into the definition of a skein-theoretic (3+1) Topological Quantum Field Theory, and give some elementary properties of this TQFT. This is joint work with Francesco Costantino, Nathan Geer and Bertrand Patureau-Mirand.

The categories of $n$-cobordisms are among the most studied objects in low dimensional topology. For $n=2$ we know that $2\operatorname{Cob}$ is a monoidal category freely generated by its commutative Frobenius algebra object: the circle. This result also classifies all TQFT functors on $2\operatorname{Cob}$. In this talk I will present similar classification results for special categories of 3- and 4-cobordisms. Here Frobenius algebra is replaced by a so-called Bobtcheva-Piergallini Hopf algebra. The results are obtained in collaboration with Marco De Renzi, Ivelina Bobtcheva and Riccardo Piergallini.

Past events

21 November 2022 (Paris)

13 March 2023 (Dijon)

5 June 2023 (Paris)

13 November 2023 (Dijon)