Khovanov homology and Wall's stabilization problem

May 24, 2023
In dimension four, the differences between continuous and differential topology are vast but fundamentally unstable, disappearing when manifolds are enlarged in various ways. Wall-type stabilization problems aim to quantify this instability. I will discuss an approach to these problems that uses Khovanov-type homology theories and relies on blending theoretical calculations with intensive machine computation. Time permitting, I will discuss how one might push these techniques further and use these Khovanov-type tools for knots and surfaces to calculate Floer-theoretic invariants for associated 3- and 4-manifolds.