Abstract: 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 out of 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 parabolic gluing method, 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.

 

Link Information: Zoom Meeting

https://us02web.zoom.us/j/85893623785?pwd=Qb1LFqIZBuqQ2JDtIArgJPFaJtncLb.1

Meeting ID: 858 9362 3785

Passcode: 155237

 

Organizer: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chao-Ming Lin (NTU), Wei-Bo Su (NCU), Chung-Jun Tsai (NTU)