GT seminar: "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 this formulation is that the RG flow on field theories over the n-dimensional euclidean space becomes a simple action on factorization algebras. In this talk, we will motivate a closely related "RG flow" and the whole idea of renormalization using prefactorization algebras defined at fixed scales. We will discuss how this approach allows us to show that "topological field theories" over euclidean spaces are always renormalizable. 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 arXiv:2407.18192, joint with D.Calaque.

This is a talk in our Geometry and Topology Seminar Series.