Holomorphic Anomaly Equation for Categorical Enumerative Invariants of Elliptic Curves
发布时间：2024年11月06日
浏览次数：82
发布者: He Liu
主讲人： 何云帆（北京大学）
活动时间： 从 2024-11-07 15:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
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.
