TNT Colloquium: Hard-Core Few-Body Physics: Geometry, Symmetry and Topology [Duke]
Motivated by applications to ultracold atoms in optical traps, I will present some examples of quantum few-body models with hard-core interactions. Despite the simplicity of the interaction, these models can have surprising dynamical properties, like superintegrability or fractional statistics. In one bizarre case, these properties can be used to calculate the digits of pi in an arbitrary base! Most of these properties can be understood by looking at the geometry of configuration space. In particular, the symmetry and topology of the coincidence manifold, i.e. the locus of points in configuration space corresponding to particles in the same position, plays a critical role in extracting universal properties for few-body models with hard-core interactions.