U.S.-Japan Joint Seminar: Quantum Geometry in Dimensions 2 and 4

该奖项支持美国科学家参加将于2002年3月18日至24日在巴尔的摩约翰·霍普金斯大学举行的关于2维和4维量子几何的美日研讨会。联合组织者是约翰·霍普金斯大学的杰克·莫拉瓦教授和日本东京大学的森田茂之教授。这是数学中最重要、发展最快的两门学科。数学物理学家意识到二维和四维量子场论之间有着深刻的相似之处，但尽管二维和四维几何的数学研究受到了物理学思想的强烈影响，但这些领域有不同的根源和不同的历史。在第二个维度中，分类很容易，研究涉及到对象家族。在维度四分类是困难的，而构建新的工具来研究该主题是非常活跃的。由于历史的原因，对二维流形(族)的研究一直被代数几何的思想所主导；但是，尽管代数曲面理论的思想对四重理论产生了巨大的影响，但那里的更深层次的发展是基于非线性分析和规范理论的技术。因此，对这些主题感兴趣的研究人员群体在社会学上是非常多样化的。然而，这两个领域在拓扑学方面有着共同的基础，通过关注这些基本问题，组织者希望能有一个广为普及的、深具兴趣的项目。研讨会组织者特别努力让年轻的研究人员和研究生既作为参与者又作为观察员。与日本专家在这一领域交换想法和数据将使美国参与者能够推进他们自己的工作，并将为未来的合作项目奠定基础。研讨会信息的传播将在万维网上提供。

0089657MoravaThis award supports the participation of American scientists in a U.S.-Japan seminar on quantum geometry in dimensions 2 and 4, to be held at the Johns Hopkins University in Baltimore from March 18-24, 2002. The co-organizers are professors Jack Morava of the Johns Hopkins University and Professor Shigeyuki Morita of the Tokyo University in Japan. These are two of the most vital and rapidly developing subjects in mathematics. Mathematical physicists are conscious of deep similarities between two and four-dimensional quantum field theories, but although mathematical research in two and four-dimensional geometry has been strongly affected by ideas from physics, these fields have separate roots and separate histories. In dimension two, classification is easy, and research is concerned with families of objects. In dimension four classification is difficult, and the construction of new tools to study that topic is very active. For historical reasons, research on (families of) two-manifolds has been dominated by ideas from algebraic geometry; but while ideas from the theory of algebraic surfaces have had great impact in four-mainfold theory, the deeper developments there have been based on techniques from nonlinear analysis and gauge theory. The population of researchers interested in these subjects is thus sociologically very diverse. However, the two fields share common foundations in topology, and by keeping these fundamental issues in focus, the organizers hope for a broadly accessible program of deep interest. Seminar organizers have made a special effort to involve younger researchers and graduate students as both participants and observers. The exchange of ideas and data with Japanese experts in this field will enable U.S. participants to advance their own work, and will set the stage for future collaborative projects. Dissemination of information on the seminar will be available on the World Wide Web.