| Résume | The famous relation between stability of holomorphic vector bundles and existence of Hermitian Yang-Mills connections can be demonstrated using Yang-Mills flow. Motivated by this theory and mirror symmetry, Thomas-Yau conjectured a stability condition for Lagrangian mean curvature flow which detects when the flow wants to break up the Lagrangian. When such break up occurs in the flow it is expected to be a singularity called a neck pinch. I will report on joint work with F. Schulze and G. Szekelyhidi which shows that, for Lagrangian surfaces, Thomas-Yau stability does indeed rule out neck pinch singularities breaking up the Lagrangian along the flow. |
