Principal Investigator: Nora Ganter
The project investigates the interaction of elliptic cohomology with other areas of mathematics and physics, with a focus on equivariant phenomena and power operations. Subjects treated range from orbifold models in string theory over representation and character theory in 2-categories to generalized Moonshine and stable homotopy theory. Hopkins-Kuhn-Ravenel character theory arose in the context of homotopy theory and exposes many formal similarities between the above fields. The goal of the project is to better understand the mechanisms underlying these observations. Power operations in elliptic cohomology were already linked to product formulas in string theory and to the twisted Hecke operators of generalized Moonshine. This project will further pursue these connections, aiming to clarify the links between the literature in these three subjects.
In less technical terms: Elliptic cohomology is a rich mix of areas of mathematics and physics, which on the surface do not appear to have much to do with each other. Especially in the presence of an action by a group of symmetries, one can observe many analogies between seemingly unrelated research areas. With collaborators from various fields of mathematics, this project seeks to find an explanation for the deeper mechanisms underlying these phenomena.
