Agnès Gadbled: Toric constructions of monotone Lagrangian submanifolds in ℂℙ^2 and ℂℙ^1×ℂℙ^1

In a previous paper, I proved that two very different constructions of monotone Lagrangian tori are Hamiltonian isotopic inside \(\mathbb{CP}^2\) by comparing both of them to a third one called modified Chekanov torus. This modified Chekanov torus has an interesting projection under the standard moment map of \(\mathbb{CP}^2\) and motivates a method of construction of (monotone) Lagrangian submanifolds in symplectic toric manifolds. I will explain how this method gives some old and new monotone examples in \(\mathbb{CP}^2\) and \(\mathbb{CP}^1 \times \mathbb{CP}^1\).