9504919 Tahvildar-Zadeh The proposed research is in the area of mathematical physics and deals specifically with regularity and stability theory of wave maps. Wave maps are a hyperbolic analogue of harmonic maps, where the domain is a Lorentzian manifold rather than a Riemannain manifold. When one considers the energy functional for maps from a Lorentzian manifold to a Riemannian manifold, the resulting Euler-Lagrange equations become hyperbolic - for maps between two Riemannian manifolds these equations are elliptic. Wave maps are called sigma models by physicists, and they arise in modern physics in various guises. For example, Einstein's field equations can be reduced to sigma model equations. Not much general theory has been developed for wave maps thus far as hyperbolic partial differential equations are mathematically harder to deal with than the elliptic ones.
