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Equivariant Cohomology is the cohomology theory of spaces acted on by groups. It can be seen as a generalization of group cohomology and ordinary cohomology. The Equivariant Cohomology of spaces is particularly nice when the space meets various technical conditions. The moment map is a map which (often) occurs when Lie groups act on varieties, or symplectic manifolds in particular ways. These momentum maps allow one to combinatorially compute the equivariant cohomology of many spaces by thinking about the one skeleton of moment graphs like Morse functions. After covering this the remainder of the talk will cover some ideas for how to approach computing the equivariant cohomology for spaces which aren't 'nice'.

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