Although a precise conjecture about the link between the existence of extremal Kähler metrics and algebro-geometric notions of stability of a polarized variety has been proposed by Yau, Tian and Donaldson, experts do not expect its complete resolution for at least another decade. However, remarkable progress is being made all the time including the verification of one direction of the conjecture through the work of Chen-Tian, Donaldson, Mabuchi and Szekelyhidi-Stopa. Moreover, advances continue to be made on important subcases and in the development of new techniques. The main objective of the workshop is to bring together leading experts in the separate but related fields of geometric analysis, differential geometry and algebraic geometry to focus on a specific, hard problem at the forefront of current research. Gang Tian (Princeton & Peking) will give a series of Aisenstadt Chair lectures.