Locality Galois Group of Meromorphic Germs in Several Variables

Explore a 45-minute lecture on the locality Galois group of meromorphic germs in several variables, presented by Sylvie Paycha at the Workshop on "Exactly Solvable Models" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the rich structure of meromorphic germs with linear poles in multiple variables, examined through the lens of locality algebras. Discover two specific classes of meromorphic germs with nested poles, originating from multiple zeta functions in number theory and Feynman integrals in perturbative quantum field theory. Learn how these classes form locality polynomial subalgebras with bases given by the locality counterpart of Lyndon words. Examine the locality Galois group, a transformation group acting on these subalgebras, and its application in providing a mathematical interpretation of Speer's analytic renormalisation for Feynman amplitudes. Investigate generalised evaluators and how the locality Galois group acts transitively on them, potentially serving as a renormalisation group in this multivariable approach. Based on joint work with Li Guo and Bin Zhang, this talk offers insights into advanced mathematical concepts at the intersection of algebra, number theory, and quantum field theory.