Isaac Wind Newell

My research focuses on nonlinear partial differential equations arising in differential geometry, in particular the problem of isometric embeddings of Riemannian manifolds in Euclidean space. The PDE system at hand is the Gauss-Codazzi system, whose type, in the case of surfaces, depends on the sign of the Gauss curvature. I am especially interested in the connections between isometric embedding and hyperbolic conservation laws, compensated compactness methods, and geometric rigidity problems. I am jointly supervised by Prof Gui-Qiang Chen and Prof Luc Nguyen.