Mayuko Yamashita: A merger of elliptic cohomology and global categorical symmetries

Abstract: In this talk, I will illustrate that the Segal-Stolz-Teichner paradigm and global categorical symmetries are starting to merge, by explaining the ongoing work with Theo Jonhson-Freyd and Daniel Berwick-Evans, titled “Extending equivariant TMF to the cusp using vertex algebras”. The spectrum “TMF”, Topological Modular Forms, is related to 2-dimensional supersymmetric quantum field theories (SQFTs). There is an equivariant refinement of TMF which reflects the group-symmetry in SQFTs. The interpretation of its variant “Tmf” has been a mystery, and its equivariant refinement has not been constructed. We provide (partial) answers to both questions using the theory of vertex operator algebras and modular tensor categories.