We restart the geometry seminar for a new academic year on 22/09, welcoming Spandan Ghosh (Oxford) to talk. The talk will take place at 2pm in the Salle des Profs (9th floor of building NO). Spandan’s title is “Lagrangian mean curvature flow out of conical singularities” and his abstract is below.
Lagrangian mean curvature flow (LMCF) is a way to deform a Lagrangian submanifold inside a Calabi–Yau manifold according to the negative gradient of the area functional. There are influential conjectures about LMCF due to Thomas-Yau and Joyce, describing the long-time behaviour of the flow, singularity formation, and how one may flow past singularities. In this talk, we will show how one may flow past a conically singular Lagrangian by gluing in expanders asymptotic to the cone, generalizing an earlier result by Begley-Moore. We solve the problem by a direct P.D.E.-based approach, along the lines of recent work by Lira-Mazzeo-Pluda-Saez on the network flow. The main technical ingredient we use is the notion of manifolds with corners and a-corners, as introduced by Joyce following earlier work of Melrose.