Ribbon concordances and slice obstructions: experiments and examples

There are 352 million prime knots with at most 19 crossings. I will discuss ongoing work with Sherry Gong showing that 1.6 million of these knots are slice (in fact ribbon) and nearly all of rest are not. Here "nearly all" means we have less than 15,000 knots ($0.004\%$) whose slice status is unknown. Because neither slice nor ribbon is known to be algorithmically decidable, we use a mix of partial techniques. I'll mention some potential applications to the slice versus ribbon conjecture and to finding exotic 4-spheres.