I will describe the derivation of a formula of Gauss-Bonnet type involving the renormalized area of a minimal submanifold of a Poincaré-Einstein space. This requires development of several new ingredients: a special compactification coming from scattering theory on the minimal submanifold, conformally invariant powers of the Laplacian and Q-curvature on submanifolds of conformal manifolds, and a conjectured analog of a celebrated result of Alexakis asserting a decomposition of integrands of conformally invariant integrals. This is joint work with Jeffrey Case, Tzu-Mo Kuo, Aaron Tyrrell, and Andrew Waldron.