2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146018This paper is based on a talk presented by the first author at the Short Program on Riemannian Geometry that took place at the Centre de Recherche Mathématiques, Université de Montréal, during the period June 28-July 16, 2004. It is a report on our joint work with János Kollár concerning the existence of an abundance of Einstein metrics on odd dimensional spheres, including exotic spheres.14 pages, Expository paper to appear in the Proceedings of the Short Program on Riemannian GeometryDifferential GeometryAlgebraic Geometrytext