Abstract: In General Relativity, Einstein's equation may be viewed as a second-order system of nonlinear PDE's for the Lorentzian metric on (n+1)-dimensional spacetime that admits an initial value formulation. The required initial data is comprised of a (usually complete) n-dimensional Riemannian manifold equipped with a symmetric (0,2)-tensor, respectively representing a spatially global "instant in time" and the "initial velocity" of the metric. The Gauss-Codazzi equations imply that not every such pair is admissible, however, and a working initial data set must satisfy certain nonlinear elliptic PDE’s dubbed the constraint equations. In this talk, I will discuss recent work with several collaborators on the construction of working asymptotically flat initial data sets in which various asymptotic features of physical interest can be prescribed.

Contact: AIM Seminar Organizers