Below is an overview of my recent research projects. They are grouped by logical connection, not by publication.

## Statistics and Sampling of Feynman periods

This is a large numerics and statistics project where we computed millions of Feynman integrals and developed a new efficient sampling algorithm to compute their average at large loop order. The resulting dataset can be a benchmark for machine learning.

## Tubing solutions to Dyson-Schwinger equations

The renormalization structure of Feynman graphs implies that the perturbative Green functions of a theory can be organized in terms of power series of rooted trees. So far, it had been tedious to recover the actual (numerical or symbolic) coefficients of an analytic Green function from those trees. We show that this can be done with a nice combinatorial operation, namely by enumerating all the tubings of the tree in question.

## Variations of Dyson-Schwinger equations

25 Years ago, Broadhurst and Kreimer gave an exact resummation of a certain Dyson-Schwinger equation, based on a single integral kernel graph. This has lead to many new insights, but the question remained to what extent the qualitative features are dependent on this particular case of truncation. In this ongoing project, I consider several types of “variations” of the DSE, in order to understand how strongly the solutions depend on details of the equation.

## Diffeomorphisms of quantum field variables

A non-linear redefinition of the field variable in a qft gives rise to complicated new interaction terms, which eventually do not contribute to the onshell S-matrix. Moreover, diffeomorphisms have the same power-counting as quantum gravity and serve as a toy model for Ward identities under such conditions.