L. Gaunce Lewis, Jr. - Recent results on Mackey functors for a compact Lie group

Mackey functors were first introduced as a tool for proving induction theorems in representation theory. They have, however, become an important tool in equivariant homotopy theory because any reasonable equivariant cohomology theory is implicitly Mackey functor valued. For applications in equivariant homotopy theory, it would be very nice to have a well-behaved extension of the notion of a Mackey functor from its original context of finite groups to the context of compact Lie groups. Unfortunately, various technical difficulties have so far severely limited the utility of the available extensions. However, the new approach to Mackey functors for a finite group taken recently by Florian Luca turns out to extend nicely to compact Lie groups. The effectiveness of this extension of his methods to compact Lie groups will be illustrated in this talk by presenting its implications for the structure of the spectrum of a commutative Mackey functor ring.