Jean-Philippe Chassé (ETH Zurich) will speak in the geometry seminar at 2pm on Monday 20th January. Jean-Philippe’s title is “Towards the Lagrangian C^0 flux conjecture” and his abstract is below.
In this talk, I will be interested in some local topological property of the Hamiltonian orbit of a Lagrangian submanifold L: is there a neighbourhood U of L in M such that whenever a Hamiltonian isotopic Lagrangian L’ is in U, then there is a Hamiltonian isotopy from L to L’ supported in U? On the one hand, I will answer the question in the positive for a large class of Lagrangians respecting some rationality condition. On the other hand, I will construct a negative answer in any symplectic manifold of dimension at least 6. Finally, I will explain how answering this question (dis)proves certain cases of the Lagrangian C^0 flux conjecture, which states that the Hamiltonian orbit of a Lagrangian should be closed in the classical Hausdorff metric. This is based on joint work with R. Leclercq, M. Atallah, and E. Shelukhin.