I will give an overview of the theory of Categorical Enumerative Invariants (CEIs), as developed in joint work with Junwu Tu and Kevin Costello. The emphasis will be on the role played by the Givental group, which controls the effect of changes of splitting on the CEIs.
If time allows I will state two new conjectures which relate the derived category of the nodal cubic with the classical $\lambda_g$ conjecture in Gromov-Witten theory, due to Getzler, Faber and Pandharipande. The new work is joint with Weng-Him Cheung and Yunfan He, and builds on work of Yefeng Shen and Junwu Tu (unpublished).