Geometry of interfaces: topological complexity in biology and materials

The geometrization of physics, which views physical phenomena through the prism of geometry and topology, has left a lasting imprint on many areas of physics, from Einstein's revolutionary adoption of Riemannian geometry to build his theories of relativity, to the rapidly multiplying zoo of topological phases in quantum physics. It is therefore not surprising that newer areas of condensed matter research, particularly synthetic and biological soft liquid crystalline matter and related materials, are best explored using the tools of low-dimensional geometry and topology. This realization is not new...