Differential Geometry
Summary
Differential geometry first arose as a mathematically rigorous framework for certain constructions in theoretical physics. It has evolved into a systematic generalization of Calculus to non-Euclidean settings, including spheres and tori. As such, it concerns geometric structures on smooth manifolds. Such structures include Riemannian metrics, symplectic forms, and more general reductions of structure groups. Symplectic geometry and (pseudo-)Riemannian geometry are the mathematical languages of classical mechanics and general relativity, respectively. At USU, research in differential geometry includes the themes of exterior differential systems, geometric analysis, integrable systems, mathematical relativity, and symplectic geometry
Faculty