Physics often reveals surprising simplicity hidden inside complicated systems. Familiar examples include the structure of Feynman amplitudes and cosmological correlators, the simplifications appearing in large-N and duality limits, and the organizing power of symmetries. In this colloquium I introduce a framework based on tame geometry that allows such simplifications to be quantified through a notion of complexity. The key principle is finiteness: the information required to specify the functions and domains describing a theory or an observable is finite. Because the framework is very general, it applies to essentially any physical quantity. This allows us both to study complexity within individual Quantum Field Theories and to investigate the structure of the space of such theories. I will present several applications and explain how this viewpoint connects to expectations for effective theories compatible with Quantum Gravity.
Professor Thomas W. Grimm is a Full Professor at Utrecht University. He is currently appointed as a Visiting Professor at Harvard University. His research is driven by the question of how quantum field theories can be unified with gravitational theories into a fundamental theory of quantum gravity. By pursuing this unification, he aims to uncover its potential phenomenological implications and explore the mathematical structures required to build its foundation. String theory serves as the main framework in this endeavor, and over the years, he gained much experience in studying the quantum field theories that arise from it.