These eight papers have been presented by mathematicians and physicists addressing special meetings at the Woods Hole Oceanographic Institution starting in 1998. The papers describe contemporary mathematics and physics, but they also describes such topics of interest to oceanography as the secondary structure of proteins and an overview of arc complexes with proposed applications to macromolecular folding. Topics include quantizing Teichmuller spaces using graphs, indices and relative indices on contact and CR- manifolds, and biologic. They include operads, moduli of surfaces and quantum algebras; fragments of nonlinear Grothendieck- Teichmuller theory, and cell decomposition; and compactification of Riemann's moduli space in decorated Teichmuller theory. The collection concludes with papers on spatial intermittence in two-dimensional turbulence using a wavelet approach and an elementary definition of Brownian motion in Hilbert space.