Topological Hochschild homology

Oberdieck and Pixton proved in their work that the generating series of Gromov-Witten classes of elliptic curves are cycle-valued quasimodular forms, and they satisfy a differential equation called holomorphic anomaly equation. We show that the generating series of categorical invariants of elliptic curves also satisfy the HAE with the assumption of their quasimodularity. This is based on joint work with Andrei Caldararu and Junwu Tu.