Georgios Dimitroglou Rizell: The nearby Lagrangian conjecture for the two-torus

In recent joint work with E. Goodman and A. Ivrii we
establish several classification results for two-dimensional
Lagrangian tori inside four-dimensional symplectic manifolds. Notably,
we establish the nearby Lagrangian conjecture in this context, which
can be formulated as follows: In canonical action-angle coordinates,
any Lagrangian torus which is homotopic to a torus of constant action
is Hamiltonian isotopic to such a torus.