Bordered Perspectives on Exotic Phenomena in 4D

In this talk, I will describe some joint works with Jesse Cohen and Sungkyung Kang. In short, these projects revolve around using tools from bordered Floer homology to distinguish exotic surfaces and contractible 4-manifolds.  The game is to try dice the objects of interest into simple pieces. First, I will describe a method for understanding certain symmetries of the Floer complex of certain knots in terms of symmetries of the Floer complexes of their complements. Kang and I refer to this as the ``LOT correspondence’’, and I will say a few words about using this correspondence to generate stably exotic corks. Second, I will describe work with Cohen which concerns interpreting certain cobordisms in terms of immersed curves. From this perspective, we explore how exotic surfaces can be constructed by studying satellites of slice disks.