From open to closed strings at genus one

In this talk I will discuss relations between the low-energy expansions  of open- and closed string amplitudes. At genus zero, it has been shown that the single-valued map of MZVs maps open-string amplitudes to their closed-string counterparts. After reviewing this story, I will discuss recent work at genus one which aims to define a similar mapping from the open to the closed string. Our construction is driven by the differential equations and degeneration limits of certain generating functions of string integrals and suggests a pairing of integration cycles and forms at genus one - analogous to the duality between Parke-Taylor factors and disk boundaries at genus zero. Finally, I will discuss the impact of said mapping on the elliptic MZVs and modular graph forms which arise naturally upon solving these differential equations.