The Penrose Inequality: An Application of Geometric PDEs to Physics

In this talk, I will discuss a conjecture of Penrose, which asserts a lower bound on the mass of a spacetime in terms of the area of a suitable horizon. Whilst Penrose presented a physical motivation for this inequality in the 1970s, the only proofs heavily rely upon PDE arguments, and in particular the use of geometric flows. I hope to show in this talk, through this concrete example (and without unpleasant technical details!), how ideas from geometric PDE theory can be helpful in obtaining results in physics.