Description:The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community. The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999. As a service to the mathematics community, the editors of the Journal of Differential Geometry decided to organize a conference to be held every three years. Among the speakers at our first conference were people working in algebraic geometry, mathematical physics and other interesting fields. These speakers are prominent specialists in their respective areas who are able to give a broad overview of recent trends and make predictions and suggestions for future research. We believe that these conferences are important gatherings that inspire experts and non-experts alike. Our first conference was held at Harvard University from April 27-29, 1990, was made possible by the generous funding of the Journal of Differential Geometry. Central to the success of this conference were the speakers who prepared not only two hours' worth of lectures, but also the manuscripts published here. Their lectures were enthusiastically received by several hundred participants.