The governing PDE's for nonlinear material's science, conformal geometry and the Hilbert-Smith Conjecture

The governing equations for the theories of conformal geometry and nonlinear materials science are basically the same and have been much studied for centuries. Despite some significant advances in the theory of these nonlinear elliptic equations there is still much to be considered. Here we discuss a little of what is known about these equations leading to a fascinating connection with Hilbert's fifth problem on Lie groups.
This talk will cover a broad sweep of modern mathematical ideas and connections between analysis, PDE, geometry, algebra and group theory painted with a broad brush.