Abstract

Lagrangian mean curvature flow (LMCF) is a canonical way to deform Lagrangian submanifoldsin CalabiYau manifolds, with the goal of finding special Lagrangians, which are volume-minimizerswithin their homology classes. Despite its significance, the general long-time behavior of LMCFremains open. In this talk, l will present recent joint work with Chung-Jun Tsai and Albert Woodwhere we construct a long-time solution to LMCF with an infinite-time singularity, precisely modeledon shrinking Lawlor necks at a specific rate. Our approach utilizes a parabolic gluing construction.inspired by Brendle and Kapouleas' work on ancient Ricci flow.