Binary tubings and Dyson-Schwinger equations - Nick Olson-Harris

Title: Binary tubings and Dyson-Schwinger equations

Abstract: Dyson-Schwinger equations are integro-differential equations satisfied by correlation functions in quantum field theory, which play the role of the "equations of motion" of the theory. They have a recursive, tree-like structure which enables these equations and their solutions to be studied combinatorially. Marie and Yeats showed that in a special case, the solution could be expanded as a sum over connected chord diagrams; this was generalized to many more cases by Hihn and Yeats. Using Hopf algebra techniques we give new combinatorial expansions for a much larger class of Dyson-Schwinger equations and systems as sums over rooted trees equipped with a kind of recursive decomposition we call a "binary tubing". This talk is based on joint work with Paul-Hermann Balduf, Amelia Cantwell, Kurusch Ebrahimi-Fard, Lukas Nabergall, and Karen Yeats.