Algebraic invariants of spaces with group action

该项目位于几何学和拓扑学领域。一系列几何对象与同伦理论、表示理论和更广泛的代数有关。首先，人们可以考虑在变形下不变的不变量，但接下来人们可以使用更多的几何方法来建立代数不变量。在某些情况下，这两种方法会收敛，在代数环境下可以建立一个完备的模型。这是在这样一个事实的背景下进行的，即等变同伦理论现在已经被很好地理解并准备好进行这种处理。其目的是提供方便的计算方法，并获得广泛的结构特征。在这种特殊情况下，检验的是能否完成计算。例如，人们可以沿着德怀尔和威尔克森的路线寻求一种更高的史密斯理论的形式。

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.