Joint IAS/Princeton University Symplectic Geometry Seminar

First, I will discuss a proof that a Lagrangian torus in \(\mathbb{CP}^2\) arising from a semitoric system described by Weiwei Wu coincides with the image in \(\mathbb{CP}^2\) of Chekanov's exotic Lagrangian torus in \(\mathbb R^4\). I will then turn to what can be regarded as higher-dimensional versions of Wu's torus, which include a monotone Lagrangian torus in \(\mathbb{CP}^3\) which is not isotopic either to the Clifford torus or to any of Chekanov and Schlenk's twist tori, as well as monotone Lagrangian submanifolds of \(\mathbb{CP}^n\) for \(n\) at least \(4\) which (unusually for monotone Lagrangians) are Hamiltonianly displaceable. This is joint work with Joel Oakley.