Probabilistic interpretation of quantum field theories

We will report on a series of recent results by Guillarmou, Kupiainen, Rhodes and others on the probabilistic construction of the 2D Liouville quantum field theories. We will cover Segal’s axioms and their probabilistic implementation in the context of the free field. If time permits, we will discuss the kind of problems arising when constructing interacting field theories, as well as the link to conformal field theories and the Virasoro algebra.