TQFT and Knot Theory

Liste des Contributions

1. Introduction to non semi-simple TQFT

Prof. Christian BLANCHET

22/04/2026 13:30

A Topological Quantum Field Theory in dimension 2+1 assigns to a
surface a vector space (states), together with an action of mapping classes and more
generally cobordisms. This includes invariants of 3-dimensional manifolds
(correlation functions) possibly decorated with links or colored graphs. The starting
point was the interpretation by Witten in the late 1980’ of the Jones...

3. TQFTs for physics

Dr Giovanni RIZI (IHES)

22/04/2026 15:00

In this talk I will discuss some instances of how Topological Quantum Field Theories (TQFTs) appear and are used in high-energy physics contexts. TQFTs describe gapped phases of Quantum Field Theories (QFTs) and their relation with generalized symmetries makes them a useful classification tool for such phases. I will also highlight instances in which TQFT tools are useful beyond classification...

2. Towards a homological reconstruction of TQFTs

Dr Jules MARTEL (Université de Cergy-Pontoise, Pontoise, France)

22/04/2026 16:30

TQFTs are the idea of Witten that we can study quantum field theories from the point of view of the topology of state spaces and of topological transitions. Mathematically, it was formalised by Atiyah as a linearization of a cobordism category. It was concretely realized by Reshetikhin--Turaev (RT) coupled with Blanchet--Habbeger--Masbaum--Vogel universal construction. The RT philosophy relies...