Conclusions

Abstract

The perspective in this book arises from several decades of experience studying the importance of boundaries for various dynamical or complex systems: drops, clusters, exotic nuclei, swimming cells, etc. We have tried to present a coherent view of the common features of the boundary in the arts and sciences, mainly using a mathematical language. The list of topics demanding a serious study of the dynamics of boundaries is much longer than we have presented here. Among many intriguing new domains of research not mentioned here, we could consider fractal boundaries, the dependence of the shape of the boundary of a collectivity as a function of the strength of the interaction between its members, the importance of the axon membrane in memory processes, biological systems with free boundaries, patterns in the universe, tumor growth, coating flows, boundaries of pseudo-manifolds and non-manifolds (for example, systems that are partially 3D and partially 2D, or even 1D), biological morphogenesis, dynamics of the benthic boundary layer modeled as a framed bordism, and so on.