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

本奖项支持美国科学家参加于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Jack Morava教授和日本东京大学的Shigeyuki Morita教授。这是数学中最重要和发展最快的两个学科。数学物理学家意识到二维和四维量子场论之间的深刻相似性，但是，尽管二维和四维几何的数学研究受到物理学思想的强烈影响，但这些领域有各自的根源和各自的历史。在二维中，分类很容易，研究对象的族。在四维分类比较困难的情况下，构建新的工具对这一课题的研究非常活跃。由于历史原因，二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主理论产生了重大影响，但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，对这些课题感兴趣的研究人员在社会学上是非常多样化的。然而，这两个领域在拓扑学上有共同的基础，通过关注这些基本问题，组织者希望能有一个广泛的、有深度兴趣的项目。研讨会组织者特别努力让年轻的研究人员和研究生作为参与者和观察员。与该领域的日本专家交流想法和数据将使美国参与者能够推进自己的工作，并为未来的合作项目奠定基础。关于讨论会的资料将在万维网上分发。

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.