We want to focus on billiard inside polyhedron and theirs geometry.

We will work on the following subjects:

• Periodic billiard trajectory inside the tetrahedron: can we characterize tetrahedra which have a periodic orbit of length 4 ?
• Linear flow on the surface of a polyhedron.
• Periodic biliard trajectories inside rational polyhedra, following the recent work of Kedlaya et. al.