Mathematical Sciences: Conference in Algebraic Topology and Homotopy Theory, August 1987, Durham, New Hampshire

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This project is a five-day conference in Algebraic Topology and Homotopy Theory to be held during August of 1987 at the University of New Hampshire, Durham, New Hampshire. Rapid and deep developments indicate a definite need for a conference of this sort in order that researchers meet and exchange ideas. It is expected that the conference will draw mathematicians from the U.S., Great Britain, France, and the Federal Republic of Germany. Topics that will be discussed include applications of simplicial methods, classical homotopy theory, cohomology of groups, stable homotopy theory, and applications of extraordinary theories. For example, the work of H. Miller on the Sullivan conjecture and its offshoots has led to some understanding of maps between classifying spaces. In addition, related work of Lannes and others has made new breakthroughs in the cohomological description of spaces of maps. It is very likely that these results will lead to even more exciting and basic theorems. Other examples include the work of Devinatz, Hopkins, and Smith in the direction of Ravenel's nilpotence conjectures. The results here indicate a glimmering of some global understanding of the stable homotopy groups of spheres.