Recorded 26 October 2021. Martin Taylor of the Imperial College London presents "The nonlinear stability of the Schwarzschild family of black holes" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos--Holzegel--Rodnianski on the linear stability of the Schwarzschild family. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-mathematical-and-numerical-aspects-of-gravitation/?tab=schedule