The main objective is to understand in more detail the singularities forming under the Lagrangian mean curvature flow, in particular the formation of type-II singularities. We will focus on the following three sub-projects related to singularities of the Lagrangian mean curvature flow.

1. Harnack inequalities for translating solitons and classifications of graphical translating solitons.

2. Singularities of Lagrangian mean curvature flow of equivariant Lagrangian submanifolds.

3. Classification of type-II singularities forming under the Lagrangian mean curvature flow of immersed spheres with non-negative Ricci curvature.