Classification results for two-dimensional Lagrangian tori

Princeton/IAS Symplectic Geometry Seminar
Topic:Classification results for two-dimensional Lagrangian tori
Speaker:Georgios Dimitroglou-Rizell
Affiliation:University of Cambridge
Date:Thursday, April 7
Time/Room:11:00am - 12:15pm/S-101
Video Link:https://video.ias.edu/puias/2016/0407-Dimitroglou-Rizell

We present several classification results for Lagrangian tori, all proven using the splitting construction from symplectic field theory. Notably, we classify Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy; they are either product tori or rescalings of the Chekanov torus. The proof uses the following results established in a recent joint work with E. Goodman and A. Ivrii. First, there is a unique torus up to Lagrangian isotopy inside the symplectic vector space, the projective plane, as well as the monotone $S^2 \times S^2$. Second, the nearby Lagrangian conjecture holds for the cotangent bundle of the torus.