Mathematical Sciences: Elliptic Genera and Elliptic Cohomology

兰德韦伯教授将继续他的椭圆 类和椭圆上同调，与R. E. Stong（弗吉尼亚大学）和其他同事。 一个新 族的周期上同调理论被证明存在于 1986年，与Stong和D. C. Ravenel;他们的 系数环是2级模函数的环。 现在广泛认识到的主要问题是确定 这些上同调理论的内在几何性质。 最近，F. Hirzebruch定义了N层椭圆形属（N 至少2），其中N = 2成为椭圆形的一般领导 椭圆上同调;它的目的是研究这些属在 详细 玉之井教授将研究内部无限 Kaehler上椭圆亏格的维数对称性 具有不同专业程度的流形。 他拟 探索这些对称性的拓扑应用， 来研究它们所隐含的精细刚性特性。 他 用仿射表示理论来研究这些问题 李代数 两位调查员都带来了 代数理论承担的问题，在几何 流形 应用包括弦理论， 被认为是量子物理学的一种有前途的方法， 相互作用的粒子系统。

Professor Landweber will continue his study of elliptic genera and elliptic cohomology, a joint project with R. E. Stong (University of Virginia) and other colleagues. A new family of periodic cohomology theories was shown to exist in 1986, in joint work with Stong and D. C. Ravenel; their coefficient rings are rings of modular functions of level 2. The main problem, now widely recognized, is to determine the intrinsic geometric nature of these cohomology theories. Recently, F. Hirzebruch has defined level N elliptic genera (N at least 2), which for N = 2 become the elliptic genera leading to elliptic cohomology; it is intended to study these genera in detail. Professor Tamanoi will study the internal infinite dimensional symmetries present in elliptic genera on Kaehler manifolds with varying degrees of speciality. He proposes to explore the topological applications of these symmetries, and to study refined rigidity properties implied by them. He approaches these problems via representation theory of affine Lie algebras. Both investigators are bringing highly sophisticated algebraic theories to bear upon problems in the geometry of manifolds. Applications include the theory of strings, which has been offered as a promising approach to quantum physics of systems of interacting particles.