Recorded 29 October 2021. András Vasy of Stanford University presents "The black hole stability problem" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: I will discuss analytic and geometric tools that lead to the understanding of black hole stability with a positive cosmological constant (Kerr-de Sitter spacetimes) and their extensions for making progress on the vanishing cosmological constant case (Kerr). This is based on joint work with Dietrich Haefner and Peter Hintz. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-mathematical-and-numerical-aspects-of-gravitation/?tab=schedule