Topological Elliptic Genera

There is a classical notion of elliptic genera, which assigns Jacobi forms to SU-manifolds. In this talk, I explain my work with Ying-Hsuan Lin (in preparation) to give its homotopy-theoretical refinements and variants, which we call "topological elliptic genera". The codomain becomes genuinely equivariant twisted Topological Modular Forms. In this talk, I explain the construction and physical idea behind, and discuss an application where we derive an interesting divisibility result of Euler numbers for Sp-manifolds.