Victor Carmona: Not too little discs and TQFTs

Abstract: The celebrated approach to perturbative QFTs proposed by K.Costello and O.Gwilliam uses factorization algebras as the main algebraic device to encode algebras of observables. An important point about their theory is the use of an effective Wilsonian formulation. In this talk, we will motivate somehow the effective point of view using prefactorization algebras defined at fixed scales. We will discuss how this approach allows us to show that "topological field theories" over euclidean spaces at a fixed scale propagate to every scale. As an application, we will explain how this can be used to construct the canonical deformation quantization of constant Poisson structures via discrete models. Time permitting, we will address what happens when the theory has defects. This talk is based on joint work with D.Calaque.