Consider a Riemannian metric on the hemisphere $S_+^n$ which has scalar curvature at least $n(n-1)$ and agrees with
the standard metric in a neighborhood of the boundary. It was conjectured by Min-Oo that any metric with these properties
must be isometric to the standard metric on the hemisphere. This conjecture is inspired by the positive mass theorem in
general relativity, and has been verified in many special cases. In this lecture, I will discuss the background of Min-Oo's
conjecture, and give a survey of various rigidity results involving scalar curvature. I will then describe joint work with
F.C. Marques and A. Neves, which gives a complete answer to Min-Oo's Conjecture in dimension $n \geq 3$.
Dec. 1st, Wednesday, 5:00-6:00 pm
Tea will be served at 4:30pm