Title: Genus-one double ramification cycles via Picard functors

Abstract: The Double Ramification (DR) cycle parametrizes, within the moduli space of smooth curves, the locus of curves paired with a principal divisor. Gromov-Witten theory is needed to define this cycle within the moduli space of stable curves. Using this definition and localization techniques, Janda, Pixton, Pandharipande and Zvonkine provide a surprising relation expressing the DR cycle using moduli of roots of the structure sheaf. In this talk we provide a definition of the DR cycle on the moduli space of smooth curves using David Holmes description of Néron models of the Jaconian over moduli of curves of dimension greater than one. We compute this cycle in genus one and match Janda-Pandharipande-Pixton-Zvonkine formula. (This is work in collaboration with David Holmes.)