Some progress towards the conjecture of Schoen

It is a classical result that on a compact manifold with non-positive Yamabe invariant, metrics with non-negative scalar curvature must be Ricci flat. It is conjectured by Schoen that the similar rigidity also holds for metrics with high codimension singularity. In this talk, we will talk about some recent progress. This is based on joint work with L.-F. Tam and J. Chu.