# Lagrangian submanifolds of complex projective space

 Princeton/IAS Symplectic Geometry Seminar Topic: Lagrangian submanifolds of complex projective space Speaker: Michael Usher Affiliation: University of Georgia Date: Friday, December 13 Time/Room: 1:30pm - 2:30pm/Fine 322, Princeton University

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.