Abel-Jacobi theory on the Picard stack

Abel-Jacobi theory provides a criterion in terms of periods to test whether divisors on curves are linearly equivalent. We will study the associated cycle over the Picard stack. The main result is a complete formula for the class of this cycle in the tautological ring parallel to Pixton's formula for the double ramification cycle. Some consequences for the moduli of differentials will be discussed. Joint work with Bae, Holmes, Schmitt, and Schwarz.