Randall Kamien

My research interests center on problems in soft condensed matter theory.

Materials Geometry

Landau theory, broken symmetry, and Goldstone modes are the lynchpins upon which our understanding of material properties rely.  While linear realizations of symmetries along with harmonic energies provide the starting point for an analysis of relevant perturbations and anharmonic elasticity, geometry provides a different framework to characterize both ground states and their deformations.  We seek to exploit geometric tools in order to capture the behavior of soft matter. 

Topological Defects

Topology turns geometry into counting.  Boundary conditions in systems with broken symmetries give rise to quantities that, upon smooth evolution of the system, remain invariant.  The properties and structures of these topological quantities have been elegantly summarized by the use of homotopy theory, a branch of algebraic topology.  Nonetheless, even common materials, like crystals, have defect structures for which homotopy theory fails to fully describe their combination and transformation.  We seek new tools and invariants to study these systems.