Iterated integrals and zeta generators

String theory scattering amplitudes on a genus-one surface involve non-holomorphic modular forms in their low-energy expansion. These can be represented by iterated integrals over holomorphic Eisenstein series and have a close connection to multiple zeta values and other periods as studied in particular by Brown. I will explain the basic ideas and the role played by derivation algebras in this connection. Mainly based on 2403.14816 and 2406.05099.