Kaehler and Sasakian Geometry, June 2009, Rome, Italy

这项提议旨在为参加2009年将在意大利罗马举行的国际会议的美国与会者提供旅费支持。会议的主题将是Kahler和sasaki几何。这两种几何风格目前为我们提供了证明爱因斯坦度量在许多光滑紧致流形上存在的最佳方法。该项目的主要智力价值源于会议的方式，该会议有望导致全球微分几何这些不同但密切相关的领域的主要研究人员之间的关键技术见解交流。国际会议在纯数学和理论物理的发展中都起着关键作用。的确，可以毫不夸张地说，一项新思想或新技术的真正重要性，只有在这样一个国际会议上得到突出对待之后，才真正成为广泛的共识。因此，罗马会议将提供一个重要的机会，以突出最近美国数学家在研究爱因斯坦的欧几里得签名引力场方程方面做出的突破性贡献。这个主题代表了数学领域之间相互作用的一个重要领域，如拓扑学和偏微分方程，而且对量子引力和弦理论等理论物理领域具有深远的影响。因此，罗马会议将不仅在数学家和物理学家之间，而且在美国和外国科学家之间，带来一次活跃的思想交流。

This proposal seeks travel support for the US participants at an international meeting thatwill 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 uswith 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 mathematicsand 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 broadconsensus 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.