We discuss computations and data regarding ribbon concordances of knots of up to 19 crossings.

Instanton Floer homology groups are groups associated to a 3-manifold. Their construction involves a process analogous to Morse theory where we consider a functional on the space of SU(2) connections on the manifold and study its critical points and gradient flow lines. In these two talks, we'll define the instanton Floer homology and discuss how to use it to understand 3-manifolds, knots, and links.