Recorded 28 October 2021. Igor Rodnianski of Princeton University presents "On the characteristic gluing problem" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: I will discuss recent joint work with S. Aretakis and S. Czimek where we studied the problem of gluing together two sets of characteristic data for solutions of the Einstein vacuum equations. This is the null analog of the Riemannian problem in which a similar question is investigated for the solutions of the space-like constraint equations. The former problem turns out to of a different nature and, interestingly enough, has application to the latter. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-mathematical-and-numerical-aspects-of-gravitation/?tab=schedule