Romain Gicquaud:Solutions to the Einstein constraint equations

Constructing solutions to the Einstein constraint equations is an important issue since they provide initial data for the Cauchy problem in general relativity. Until quite recently, the only methods known to construct solutions to the Einstein constraint equations were restricted to the case of constant mean curvature (or almost constant mean curvature) initial data. In this talk I will introduce the constraint equations and the so called conformal method which is one of the most powerful method to produce solutions to the constraint equations. Then I will explain recent advances with this method which provide large classes of solutions with non constant mean curvature.