Appears in collection : Tame Geometry Thematic Month Week 3 / Géométrie modérée Mois thématique semaine 3

In the first part of the talk I will sketch how tame geometry results can be of relevance in quantum systems that are described by quantum field theory. I will highlight some mathematical questions that arise in these applications. I will then turn to using tame geometry in quantum gravity, and specifically in string theory, and stress that it is a powerful framework that allows one to address finiteness questions that were posed in these fields.