GRIEG project SCREAM

Beyond Riemannian geometry, there exists an abundance of fascinating differential geometric structures, many of which are motivated by applications in pure mathematics, geometric analysis, complex analysis and physics, in particular classical field theory, relativity, string theory, geometric control theory and robotics. Only a handful of these geometries have been studied in detail. The goal of this GRIEG project at the interface of geometry, algebra and PDE is to answer questions of fundamental importance for a variety of geometric structures beyond classical Riemannian geometry. Of particular focus are the broad classes of Cartan and parabolic geometries, which include conformal, projective, CR and ODE geometry, (2,3,5)-distributions, parabolic contact structures and many more besides. These structures are the central themes of this SCREAM proposal: Symmetry, Curvature Reduction, and EquivAlence Methods.