Abstract:

The Thomas-Yau conjecture states that under a suitable notion of "stability", a "stable" Lagrangian submanifold evolving under the Lagrangian mean curvature flow (LMCF) has long time existence and flows to a unique special Lagrangian in its class. This conjecture is too good to be true as the behaviour of LMCF is much more intricate. In this talk, I will introduce key updates proposed by Joyce, some recent progress, and discuss the difficulties associated with the programme.