Harmonic analysis of elliptic systems on riemannian manifolds

Harmonic analysis is the study of waves. Radio signals, sound waves, waves on a pond, can all be investigated in terms of their harmonic frequencies. When these and other physical phenomena are expressed mathematically, it is in the language of partial differential equations. Partial differential equations also arise in the study of geometry. This project concerns the systematic development of the harmonic analysis needed to understand properties of partial differential equations on geometrical surfaces and on regions with irregular boundaries.