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Abstract:  Mackey functors were introduced by Dress and Green to encode operations that behave like restriction and induction in representation theory.  They play a central role in equivariant homotopy theory, where homotopy groups are replaced by homotopy Mackey functors.  In this talk I will discuss joint work with Dan Dugger and Christy Hazel classifying perfect chain complexes of Mackey functors for G=Z/2.  Our classification leads to a computation of the Balmer spectrum of the derived category.  It has topological consequences as well, classifying all modules over the equivariant Eilenberg--MacLane spectrum HZ/2.