Speaker
Description
Twenty-five years ago, together with Ivan Todorov, we began a long-standing research program on quantum field models with rational correlation functions. From a mathematical viewpoint, these are models with the simplest singularity structure, while physically they correspond to theories in which causal correlations propagate exactly at the speed of light. This long-standing program gave rise to several developments, some of them quite unexpected. One such direction emerged in connection with renormalization theory, the renormalization group, and ultraviolet anomalies in massless models. At the core of this relation lies an operadic structure associated with certain configuration spaces. In this talk, an overview of this line of research will be presented. In conclusion, new perspectives related to a novel type of residue calculus will be discussed, together with its impact on both the theory of vertex algebras in higher dimensions and the study of renormalization anomalies.