Finite Groups and Periodic Theories in Stable Homotopy
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The study of complex cobordism and related cohomology                   theories is a long standing and well respected area of algebraic                topology.  Another area has been that of (finite) group theoretic               constructions, becoming, in its most modern form, equivariant                   stable homotopy theory.  Results in recent years, most                          spectacularly the proofs of Segal's Burnside ring conjecture and                Ravenel's nilpotence conjecture, have dramatically begun to bring               to fruition these two branches of stable homotopy theory.                               Historically, these branches have been basically independent            of each other.  An exception is Atiyah's theorem relating K*(BG)                (a bordism type of object) to the complex representation ring of                G.  There are now indications of much more widespread                           interrelations.  This is the subject of Kuhn's recent and current               research.  It is hard to say where the study of such intricate                  algebraic patterns will lead, but the history of mathematics                    strongly suggests that mastering them will have repercussions                   elsewhere, either in use of the patterns themselves or of the                   techniques developed for treating them.
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