Meromorphic germs in several variables with linear poles arise in mathematics in various disguises. We investigate their rich structure in the framework of locality algebras, namely algebras equipped with a binary symmetric relation compatible with the operations. We focus on two classes of meromorphic germs with prescribed types of nested poles, arising from multiple zeta functions in number theory and Feynman integrals in perturbative quantum field theory respectively. They turn out to be locality polynomial subalgebras with locality polynomial bases given by the locality counterpart of Lyndon words. This enables us to explicitly describe a transformation group acting on them that we call locality Galois group.
As an application, we propose a mathematical interpretation of Speer's analytic renormalisation for Feynman amplitudes. We study a class of locality characters, called generalised evaluators after Speer. We show that the locality Galois group acts transitively on generalised evaluators by composition, thus providing a candidate for a renormalisation group in this multivariable approach.

This is based on joint work with Li Guo and Bin Zhang.