In this session, we will introduce some semiclassical analysis tools that connect quantum propagation at high frequencies to the underlying classical dynamical system. In the first half, we will do a brief refresher on notions like Hamiltonian systems, rudiments of pseudo-differential calculus, Wigner distributions and their weak limits (semiclassical measures and their refinement at two or more microlocal scales).

In the second half, we will go into some applications in the study of high frequencies of operators with degeneracies (like subelliptic operators) and, more specifically in the focus of this working group, on some recent results (Vacelet (2024), Bal, Becker, Drouot, Fermanian, Lu, Watson (2022) on the propagation of edge states along a curved interface between two topological insulators, where the solution is governed by a semiclassical Dirac operator with variable mass.