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.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/8825