University of David
At the ICM in Nice in 1970 Quillen described the theme of his previous year’s work as the cohomology of finite groups. Besides the Adams conjecture and algebraic K-theory, another fertile line of development came out of this. Quillen had shown that themod p cohomology of any compact group is controlled by the lattice of its elementary p-subgroups, proving, among other things, the Atiyah-Swan conjecture that the Krull dimension of themod p cohomology ring is themaximal rank of an elementary p-subgroup and calculating for the first time the cohomology rings of the spin groups. He was interested in using these ideas to obtain significant results in finite group theory, but quite soon he left the field to others.