Sticky particle dynamics

I will discuss the time evolution of a collection of particles that interact primarily through perfectly inelastic collisions. I will explain why this problem is tractable if the particles are constrained to lie on a line versus if they are allowed to move freely in space.  In particular, I'll also describe an equation at the heart of this difficulty which some researchers believe has been solved and others do not.  This topic has motivations in astronomy and connections with optimal mass transportation which I will touch upon if time permits.