Recorded 29 October 2021. Matti Lassas of the University of Helsinki presents "Inverse problems for Einstein’s equations and other non-linear hyperbolic equations" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: We consider inverse problems for non-linear hyperbolic equations. As an example, we consider the equation □gu+au2=fonaLorentzianmanifold(M, g).Westudythequestion,dotheobservationsofthesolutionsu|_{V}onanopensubsetV\subset M,thatcorrespondtosourcesfsupportedinV,determinethemetricginalargerdomainW\subset M,containingV.ThedomainWcanbethemaximaldomaintowheretheinformationsentfromVcanpropagateandreturnbacktoV$. In addition, we consider inverse problems for the coupled Einstein equations and matter field equations. The results have been done in collaboration with Ali Feizmohammadi, Yaroslav Kurylev, Lauri Oksanen, Gunther Uhlmann, and Yiran Wang. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/workshop-ii-mathematical-and-numerical-aspects-of-gravitation/?tab=schedule