Groups, piecewise linear representations, and linear 2-representations

This project aims to address fundamental questions at the interface of two central areas of modern mathematics geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this project include resolutions to open problems in the theory of Artin groups and the creation of a new subject: the dynamical theory of 2-linear groups.