One of a hot topic in four-dimensional topology is the study of smooth embeddings of surfaces. Since the failure of the Whitney trick underlies the distinctive behavior of differential topology in dimension four, embedded surfaces are expected to carry essential information about smooth structures on 4-manifolds. In particular, the unknotting conjecture asks whether a topologically trivial embedding of S^2 into S^4 must also be trivial up to smooth isotopy. This is a fundamental open problem, comparable in importance to the smooth four-dimensional Poincaré conjecture.

Seiberg–Witten theory is one of the strong tools in low-dimensional topology, detecting smooth information from solutions of a nonlinear partial differential equation on 3- and 4-manifolds. A variant of this theory is Real Seiberg–Witten theory. In this talk, we use Real Seiberg–Witten theory to detect an infinite family of embeddings of the real projective plane into the 4-sphere that are all topologically equivalent but pairwise distinct up to smooth isotopy. We also explain recent developments, including a satellite formula for the Real Seiberg–Witten Floer homotopy type, which is related to the computation of the invariants used in this construction.

15:10 - 16:10 Professor Miyazawa
16:10 - 16:45 Tea
16:45 - 17:45 Professor Kodera