An atomic approach to Wall-type stabilization problems

(Virtual)

In dimension four, the differences between continuous and differential topology are vast but fundamentally unstable, disappearing when manifolds are enlarged in various ways (especially through connected sums with S2xS2). I will discuss Wall's stabilization problem and some of its variants, all of which aim to quantify the instability of exotic phenomena. Guided by a connection between Wall’s stabilization problem and the famous h-cobordism problem, I will outline an “atomic approach” to addressing these problems, providing a construction of exotic 4-dimensional phenomena that are candidates to survive any prescribed number of stabilizations.