Speaker: **Mizuki Oikawa** (Univ. Tokyo)

Title: Group actions on bimodules and equivariant $\alpha$-induction

Time/Date: 4:45-6:15pm, May 16 (Tue), 2023.

Room: Room: 126 Math. Sci. Building

Abstract: In this talk, I would like to introduce the categorical reformulation of equivariant $\alpha$-induction for conformal nets. Indeed, equivariant $\alpha$-induction can be formulated as crossed functors to the tensor category of bimodules. For this, we see that a group action on a $C^\ast$-tensor category induces that on the bicategory of equivariant Q-systems, which includes bimodule categories as tensor subcategories. Moreover, we can define an appropriate notion of equivalence between bicategories with group actions in two equivalent ways, and the bicategory of equivariant Q-systems is equivalent in this sense to the bicategory of extensions of von Neumann algebras with group actions. I would also like to introduce two Q-systems that arise from equivariant $\alpha$-induction and their coincidence. This talk is based on https://arxiv.org/abs/2303.11845.