Laura Scull - Rational S¹-equivariant homotopy theory

I will discuss an algebraicization of rational S¹-equivariant homotopy theory. There is an algebraic category of ``T-systems'' which is equivalent to the homotopy category of rational S<sup>1</sup>-simply connected S<sup>1</sup>-spaces. There is also a theory of ``minimal models'' for T-systems, analogous to Sullivan's minimal algebras. Each S¹-space has an associated minimal T-system which encodes all of its rational homotopy information, including its rational equivariant cohomology and Postnikov decomposition.