Knotted surfaces in 4-space

I will give a short introduction to knotted surfaces in 4-space and discuss some recent developments. First, I will give some motivation, briefly discuss methods for distinguishing knotted surfaces (such as the Khovanov TQFT), and talk about connections with 4-manifolds. Then, I will introduce Artin’s spinning construction, variants of which were defined by Zeeman, Fox, Litherland, and Price-Roseman. Finally, I will specialize to knotted RP^2’s in S^4 and construct a knotted RP^2 in S^4 that cannot be decomposed as the connected sum of an unknotted RP^2 and a knotted S^2. This last result on RP^2’s is joint with Hughes, Kim, and Miller.