Groups, piecewise linear representations, and linear 2-representations

这个项目旨在解决现代数学的两个中心领域--几何群论和更高表示理论--之间的基本问题。高等表示理论是一个相对较新的领域，但它的工具已经对数学产生了巨大的影响。该项目预计将使用这些工具来解决几何群论中的突出问题。这个项目的预期成果包括解决Artin群理论中的公开问题，以及创建一门新的学科--双线性群的动力学理论。

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 of open problems in the theory of Artin groups and the creation of a new subject, the dynamical theory of two-linear groups.