In lieu of an abstract I offer a problem.
Consider three billiard balls of the same radius and mass,
undergoing totally elastic reflections on a billiard table
with no walls (the whole plane). All three balls can be given
non-zero initial velocities. What is the maximum (supremum)
possible number of collisions among the three balls?
The supremum is taken over all initial positions and initial velocities.
I will discuss this problem and its generalization to any finite family
of balls in one, two and higher dimensions.
Joint work with Jayadev Athreya and Mauricio Duarte.