UBC Math Department Colloquium: Sungkyung Kang

We say that two smooth 4-manifolds are exotic if they are homemorphic but not diffeomorphic. Wall's theorem, proven in 1964, says that when the given 4-manifolds are simply-connected, they are always diffeomorphic after sufficiently many stabilizations, i.e. connected-summing with S^2 \times S^2, but whether we need more than one stabilization remained mysterious for almost sixty years. In this talk, I will present the first example of an exotic pair of simply-connected 4-manifolds with a common boundary which stays exotic after one stabilization. This talk is based on my work arXiv:2210.07510, which involves a careful argument involving bordered-involutive techniques in Heegaard Floer theory, pioneered by arXiv:2202.12500 and arXiv:2207.11870 by K. and K.-Park.