Meetings: 3106 MSB from 9 to 10 on Thursdays.
Credit: The variable unit request form can be found here ad-student-handbook and should be filled out if you want course credit.

[GKM]Equivariant cohomology, Koszul duality, and the localization theorem by M Goresky, R Kottwitz2 and R MacPherson
[AB]The moment map and equivariant cohomology by M Atiyah and R Bott
[Pro]Symplectic geometry notes by N Proudfoot
[GZ]Equivariant de Rham Theory and Graphs by V Guillemin and C Zara
[TW] The cohomology rings of Abelian symplectic quotients by S Tolman and J Weitsman
[Tym]An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson by J Tymoczko
Software for computations
[Bro][Lectures on the Cohomology of Groups by K Brown
[GS]Convexity properties of the momentum mapping by V Guillemin and S Sternberg
[H] Topological properties of subanalytic sets by Robert Hardt
[E]Notes by J Erickson

Course Outline: This is a rough outline and (apart from exam dates) subject to change.
October 5Yuze LuanIntroduction
October 12Timothy PaczinskiExamples
October 19Timothy PaczinskiEquivariant Chains
October 26Jon EricksonSymplectic Actions
November 3Jon EricksonSymplectic Actions
November 10Jon EricksonSymplectic Actions
November 17Yuze LuanIntersection Homology
November 24holiday
December 1Raymond ChanEquivariant Formality
December 8Koszul Duality
January 11Jon EricksonExamples: Notes [E]
January 18Jon EricksonExamples: Notes [E]
January 25Timothy PaczinskiSubanalytic Sets [H]
February 1Timothy PaczinskiSubanalytic Sets [H]
February 8Timothy PaczinskiEquivariant Chains
February 15No Meeting
February 22Jon EricksonDerived Sheaf Categories
February 29
March 7
March 14

October 12 references:
In [Tym sec 4] there are three nice examples including the case of the projective plane as [Tym ex 4.1]. The formula in [Tym thm 3.4] used there agrees with [GKM thm 1.2.2] and is equivalent to the different looking one in [GKM thm 7.2]. These examples might also enable you to work out a couple for yourself just starting from a graph such as a polygon in the plane. The definition [GZ def 2.1.1] gives a notion of such a graph. In their notation the cohomology computation [GKM thm 1.2.2] becomes the combination of [GZ thm 1.7.1] and [GZ thm 1.7.3]. The phrasing is algebraic rather than symplectic. The definition of equivariantly formal involves a spectral sequence on which Ken Brown's book Cohomology of Groups has a very nice exposition and [Bro sec 5.1] has a shortened version.

Jon Erickson's notes for symplectic actions.