In this talk I will answer the following basic question:
What are the optimal assumptions, of geometric and analytic nature, which
guarantee that a null-solution $u$ of the Helmholtz operator $\Delta+k^2$
in an exterior domain $\Omega$ can be represented in terms of layer potentials
naturally associated with the said Helmholtz operator and given domain?
This work, at the interface between Geometric Measure Theory, Harmonic Analysis,
Scattering Theory, and Clifford Analysis, generalizes and unifies classical results
of Sommerfeld, Weyl, M\"uller, and Calder\'on. I will also explore similar issues in relation
to the Stokes system of hydrodynamics.