Building concordances

I’ll talk about two of my favorite theorems in S^4: Hirose's understanding of which surface automorphisms can be achieved through ambient diffeomorphism restricted to a subsurface, and Kervaire's proof that every 2-sphere is slice into B^5. I think the first is very underrated, and the second is a great example of how dimension 4 differs from dimension 3. I'll show how to use these theorems to perform interesting constructions in dimensions 4 and 5 (which I'll motivate a lot more in the colloquium on Friday). My work in this talk is joint with Mark Hughes and Seungwon Kim.