Algebraic invariants of spaces with group action

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The project lies in the area of geometry and topology. A range of geometricobjects are relevant arising from homotopy theory, representation theory andalgebra more broadly.To start with one may consider invariants that are invariant under feformations,but one may go on to build the algebraic invariants using more geometricmethods. In certain circumstances these two approaches converge and acomplete model can be built in an algebraic setting. This is in the context of thefact that equivariant homotopy theory is now quite well understood and readyfor this treatment. The aim is to give accessible means of calculation and accessto broad structural features. The test in this particular case is whethercalculations can be completed. For example one may seek a form of higher Smiththeory along the lines of Dwyer and Wilkerson.