Konstantin Wernli: Cutting, gluing and functoriality in perturbative scalar field theory

Speaker
Konstantin Wernli, University of South Denmark

Abstract
I will give an overview of a research program to investigate cutting and gluing – from a functorial viewpoint –  in perturbative scalar field theory. One of the main difficulties is extending renormalization to this context. First, I will talk about earlier results for the two-dimensional case, where only tadpoles (short loops) need to be regularized. Then I will present two different ideas to tackle higher-dimensional versions: a combinatorial approach where the scalar field theory lives on a graph, and a gluing formula for heat kernels. This is based on the papers arXiv:1912.11202, arXiv:2308.07801, arXiv:2404.00156 which are joint work with P. Mnev, S. Kandel, and I. Contreras.