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I will describe an inductive algorithm computing Gromov-Witten invariants in all
genera with arbitrary insertions of all smooth complete intersections in projective
space. The main idea is to show that invariants with insertions of primitive
cohomology classes are controlled by their monodromy and by invariants defined without
primitive insertions but with imposed nodes in the domain curve. To compute these
nodal Gromov-Witten invariants, we introduce the new notion of nodal relative
Gromov-Witten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande,
and Dimitri Zvonkine (arxiv:2109.13323).
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