Global wavefront propagation and non-elliptic Fredholm theory

Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop and extend remarkable new mathematical methods, involving global wavefront set analysis and Fredholm theory, that have been discovered recently to solve such equations. These methods extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-time asymptotics.