Billiard flow and eigenfunction concentration on polyhedra

This talk will have a dynamical and an analytical component. On the dynamical side, we will study the properties of the billiard flow on $3$ dimensional convex polyhedra. More precisely, we will study periodic broken geodesics not hitting a neighbourhood of the $1$-skeleton of the boundary (also called ``pockets"). On the analytical side, we will apply these results to prove a quantitative Laplace eigenfunction mass concentration near the pockets, using semiclassical tools and control-theoretic results. This is joint work with B. Georgiev and M. Mukherjee.