Kaehler and Sasakian Geometry, June 2009, Rome, Italy

This proposal seeks travel support for the US participants at an international meeting that will be held in Rome, Italy, in 2009. The topic of the meeting will be Kahler and Sasakian geometry. These two flavors of geometry currently provide us with the best methods available for proving the existence of Einstein metrics on many smooth compact manifolds. The primary intellectual merit of the project stems from the manner in which the meeting is expected to lead to an exchange of key technical insights between leading researchers in these distinct but intimately related areas of global differential geometry. International meetings play a key role in the development of both pure mathematics and theoretical physics. Indeed, it would not be an exaggeration to say that the real importance of a new idea or technique really only becomes a matter of broad consensus after it has been given prominent treatment at such an international gathering. The Rome meeting will thus offer a key opportunity to highlight the ground-breaking contributions recently made by US-based mathematicians to the study of Einstein's gravitational field equations in Euclidean signature. This topic represents an important arena of interaction between mathematical fields as diverse as topology and partial differential equations, and moreover has profound ramifications for areas of theoretical physics such as quantum gravity and string theory. The Rome meeting should thus result in a lively exchange of ideas, not only between mathematicians and physicists, but also between American and foreign scientists.