U.S.-France Seminar on Infinite - Dimensional Symmetries in Physics and Mathematics: Paris, France, June 1989

该奖项将支持美国参加将于1989年6月在法国巴黎举行的关于物理和数学中无限维对称性主题的美法研讨会。美国的组织者是麻省理工学院的辛格博士。法国同行是帕莱索综合理工学院数学中心的J. P. Bourguignon教授。研讨会将为美国和法国的数学家和物理学家提供机会，就当代数学和理论物理学中一些重要的话题进行交流。讨论的主题有：1)Virasoro代数、超Virasoro代数和仿射李代数的表示；它们的BRST上同调；扩展到任意黎曼曲面；共形代数和超共形代数的非线性推广。2)共形不变场论的分类；可积系统，量子群。3)超模空间、超积分、超紧化和泛模空间；多循环字符串图。增压算子，它的指数，以及与椭圆同调的关系。5)超弦理论，sigma模型，协集空间，尝试恢复摄动序列；微调问题和粒子现象学，普朗克长度物理学。基于相互作用世界表动力学的新弦理论。

This award will support U.S. participation in a U.S.-French seminar on the topic of infinite-dimensional symmetries in physics and mathematics, to be held in Paris, France in June 1989. The U.S. organizer is Dr. I. M. Singer of the Massachusetts Institute of Technology. The French counterpart is Professor J. P. Bourguignon, Centre de Mathematiques, Ecole Polytechnique, Palaiseau. The seminar will provide the opportunity for exchange between U.S. and French mathematicians and physicists on a number of topics of critical interest in contemporary mathematics and theoretical physics. Among the subjects for discussion are: 1) The representations of the Virasoro algebra, the super Virasoro algebra, and affine Lie algebras; their BRST cohomology; extensions to arbitrary Riemann surfaces; non-linear generalizations of the conformal and superconformal algebras. 2) The classification of conformally invariant field theories; integrable systems, quantum groups. 3) Supermoduli spaces, superintegration, supercompactifications, and universal moduli spaces; multi-loop string diagrams. 4) The supercharge operator, its index, and relation to elliptic homology. 5) Superstring theories, sigma-models, coset spaces, attempts to resum the perturbation series; fine tuning problems and particle phenomenology, Planck-length physics. New string theories based on interacting world-sheet dynamics.