How does singular structure form in matter and in spacetime?
(Tom Witten)

Drop Snapping instability

One basic behavior of matter---especially tenuous matter that can deform easily into its embedding space--- is its characteristic of creating sharp, singular spatial structure spontaneously. The vortex in a draining sink and a crumpled sheet of paper are two examples. Often these structures are fundamental consequences matter's essential nature---its local connectivity and its inertia. What is the range of this singularity-forming behavior, to what degree does it condense the system's energy into the singularity, and what analogous singularities might occur in spacetime?