Topological Elliptic Genera

by Mayuko Yamashita (Kyoto University)

Thursday 13 Feb 2025, 14:15 → 15:15 Europe/Berlin

H4 (Geomatikum)

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 (https://arxiv.org/abs/2412.02298) to give its homotopy-theoretical refinements and variants, which we call "topological elliptic genera". The codomain becomes genuinely equivariant twisted Topological Modular Forms. This work is in the context of equivariant Segal-Stolz-Teichner project. 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, as well as a further computational development in an ongoing joint work with Tilman Bauer.