Very recently, David Roberts and I have discovered wonderful conditions imposed on Feynman integrals by Betti and de Rham homology. In decoding the corresponding matrices, we encounter asymptotic expansions of a refined nature. In making sense of these, we appear to have some refuge in resurgence.

Rooted connected chord diagrams can be used to index certain expansions in quantum field theory. There is also a nice bijection between rooted connected chord diagrams and bridgeless maps. I will discuss each of these things as well as how the second sheds light on the first. (Based on work with Nicolas Marie, Markus Hihn, Julien Courtiel, and Noam Zeilberger.)