Conference on Mathematical Physics and Geometric Analysis

该奖项将支持2008年1月在加拿大多伦多菲尔兹研究所举行的为期四天的数学物理和几何分析会议的美国参与者。虽然最近的许多会议都集中在几何分析的单个方面，如辛拓扑、微局部分析或泊松几何，但迄今为止还没有一个会议将代表子领域范围的研究人员聚集在一起。这次会议将聚集各种各样不经常互动的数学家。讲座将涵盖辛几何、表示理论、微局部分析以及这些与物理学的相互作用的最新进展。着眼于未来，一个关键的目标是通过正式和非正式的讨论来确定重大的开放性问题和猜想。会议的综合性为研究生和初级研究人员提供了一个理想的机会，这在专业研讨会上通常是不可能的，可以获得几何分析广度及其与物理学关系的视角。此外，本次会议上众多的高级研究人员为初级研究人员提供了巨大的资源，可以为他们的工作寻求建议，并促进新的合作，因为他们正在从研究生院过渡到博士后职位，再到终身职位。近年来，在数学和物理的结合方面取得了广泛的进展。该奖项将使美国数学家有机会参加2008年1月在加拿大多伦多菲尔兹研究所举行的为期四天的会议，会上将介绍和讨论这些新的发展。这类会议往往是形成新的合作和开展新的研究倡议的论坛。因此，这次会议的主要影响是在受物理学强烈影响的各种数学领域的发现和理解的进步。

This award will support U.S. participants at a four-day conference on Mathematical Physics and Geometric Analysis in January, 2008, at the Fields Institute in Toronto, Canada. While many recent conferences have focused single aspects of geometric analysis, such as symplectic topology, microlocal analysis, or Poisson geometry, none has hitherto brought together researchers representing the gamut of subfields. This conference will gather a wide variety of mathematicians who do not frequently interact. The lectures will cover a broad range of recent advances in the symplectic geometry, representation theory, microlocal analysis, and the interactions of these with physics. With an eye towards the future, a key aim is to identify the significant open problems and conjectures through formal and informal discussions. The comprehensive nature of the conference makes an ideal opportunity, not usually available at a specialized workshop, for graduate students and junior researchers to gain a perspective of the breadth of geometric analysis and its relationships with physics. Moreover, the great range of senior researchers at this conference represent a tremendous resource for junior researchers to seek advice on their work and to foster new collaborations, as they make the transition from graduate school to postdoctoral positions to tenure-track positions.There has been extensive progress in recent years at the interface between mathematics and physics. This award will allow U.S. mathematicians to participate in a four-day conference in January, 2008, at the Fields Institute in Toronto, Canada, where these new developments will be presented and discussed. Meetings of this kind are often the forum where new collaborations are formed and new research initiatives undertaken. Hence the principal impact of this conference is the advancement of discovery and understanding in the wide variety of mathematical fields that are strongly influenced by physics.