Author: J.P.C.Greenlees Institution: University of Sheffield, UK Title: Local cohomology in equivariant topology Abstract: The article describes the role of local homology and cohomology in understanding the equivariant cohomology and homology of universal spaces. This brings to light an interesting duality property related to the Gorenstein condition. The phenomena are studied and illustrated in several rather different families of examples. Both topology and commutative algebra benefit from the connection, and many interesting questions remain open.