Mathematical Sciences: Homotopy Theory

道格拉斯·C·拉弗内尔一直致力于并将继续致力于拓扑学中使用的代数技术。与美国各地的其他人合作，他阐明了有限群的分类空间的Morava K-理论，素数3的同伦型MO(8)，以及物理学家(通过弦理论)和数学家明显感兴趣的新的椭圆上同调理论。这项研究的继续还将包括球面同伦群的一些机器计算。

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.