Kaehler and Sasakian Geometry, June 2009, Rome, Italy

该提案寻求为美国参加将于2009年在意大利罗马举行的国际会议的与会者提供旅费支助。会议的主题将是卡勒和Sasakian几何。这两种几何风格目前为我们提供了最好的方法 可用于证明许多光滑紧致流形上爱因斯坦度量的存在性。该项目的主要智力价值源于会议预期将导致全球微分几何这些不同但密切相关领域的主要研究人员之间交流关键技术见解的方式。国际会议在纯理论物理学和理论物理学的发展中起着关键作用。事实上，可以毫不夸张地说，只有在这样的国际聚会上受到突出对待后，新想法或技术的真实的重要性才真正成为广泛共识的问题。因此，罗马会议将提供一个关键的机会，突出美国数学家最近在研究爱因斯坦的欧几里得签名引力场方程方面所作的突破性贡献。 这一主题代表了数学领域之间相互作用的一个重要竞技场，如拓扑学和偏微分方程，而且对理论物理领域如量子引力和弦理论有着深远的影响。 因此，罗马会议不仅应该在数学家和物理学家之间，而且也应该在美国和外国科学家之间进行热烈的思想交流。

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.