turkmath.org

Considerations from several different areas of mathematics have prompted the development of so- called higher geometry: the study of categorified analogues of geometric structures. Despite being studied for nearly two decades, few examples that capture non-abelian phenomena have been constructed. And here by "constructed", we mean to the level that would satisfy traditional differential geometers, as opposed to the kind of construction that category theorists are comfortable with.

To this end, I will describe a new framework to work with bundle 2-gerbes, which from a higher- category point of view are certain types of truncated descent data for $\infty$-stacks on a manifold. The description is sufficient to undertake concrete computations more satisfying to traditional differential geometers and mathematical physicists. I also describe explicit geometric examples that can be constructed using our framework, including infinite families of explicit geometric string structures.