Mathematical Sciences: Homotopy Theory

Douglas C. Ravenel一直致力于并将继续致力于拓扑学中使用的代数技术。在与美国其他学者的合作中，他阐明了有限群分类空间的Morava k理论，质数为3的MO(8)的同伦类型，以及物理学家（通过弦理论）和数论家明显感兴趣的一个新的椭圆上同调理论。本研究的继续将包括一些球同伦群的机器计算。

Douglas C. Ravenel has been working and will continue to work on algebraic techniques used in topology. In collaboration with various others across the U.S., he has shed light on the Morava K-theory of the classifying space of a finite group, on the homotopy type of MO(8) at the prime 3, and on a new elliptic cohomology theory of apparent interest to physicists (through string theory) and to number theorists. The continuation of this research will also include some machine computation of homotopy groups of spheres.