Propagation of singularities for weak KAM solutions and barrier functions

This paper studies the structure of the singular set (points of nondifferentiability) of viscosity solutions to Hamilton-Jacobi equations associated with general mechanical systems on the n-torus. First, using the level set method, we characterize the propagation of singularities along generalized characteristics. Then, we obtain a local propagation result for singularities of weak KAM solutions in the supercritical case. Finally, we apply such a result to study the propagation of singularities for barrier functions

The quantum spin Hall effect and topological insulators

In topological insulators, spin-orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties.Comment: 7 pages, 5 figures, an introduction of the quantum spin Hall effect and topological insulators. For a video introduction of topological insulators, see http://www.youtube.com/watch?v=Qg8Yu-Ju3V