Holomorphic Anomaly Equation for Categorical Enumerative Invariants of Elliptic Curves
Time: 2024-11-06
Published By: He Liu
Speaker(s): Yunfan He(BICMR)
Time: 15:00-16:00 November 7, 2024
Venue: Room 77201, Jingchunyuan 78, BICMR
An important property of Gromov-Witten invariants of elliptic curves is that their generating series are modular forms, and they satisfy a differential equation called holomorphic anomaly equation. Categorical enumerative invariants (CEI) are a certain type of invariants associated to an A_\infty algebra and a splitting of Hodge filtration on its cyclic homology. It is conjectured that when choosing the Fukaya category of an elliptic curve and a monodromy-invariant splitting, the CEI invariants is the same as Gromov-Witten invariants. Though this still remains as a conjecture, we show that under certain modularity assumption, the generating series of CEI invariants of elliptic curves also satisfy a similar holomorphic anomaly equation.
