VIGRE@LSU: Equivariant Cohomology seminar

On a rotating hollow sphere, there are exactly two points that don't move at all (we might call them the "north and south poles"). The sphere belongs to a large class of important topological spaces with two key features: (1) they have some (perhaps more than one) kind of rotational symmetry, and (2) they have finitely many points that don't move when the space is rotated. Equivariant cohomology, the subject of this seminar, is a powerful tool for studying the geometry of such spaces. Using equivariant cohomology, we will explore remarkable connections to combinatorics and group theory.

• D. Sage
• C. Bremer
• D. Cohen
• J.W. Hoffman
• L. Smolinsky
• M. Yakimov

• Calculation of the intersection cohomology of the egyptian pyramid (written up by Charlie Egedy)

Currently, we are reading through Macpherson's notes (2).

1. Goresky, M; Kottwitz, R; Macpherson, R. Equivariant cohomology, Koszul Duality, and the localization theorem. Invent. Math. 131 (1998), no. 1, 25--83
2. Macpherson, Robert. Equivariant Invariants and Linear Geometry. https://services.math.duke.edu/~ezra/PCMI2004/macPherson.jcp.pdf
3. Tymoczko, J. An Introduction to Equivariant Cohomology, following Goresky, Kottwitz, and MacPherson. Arxiv. [math.AG/0503369]
4. Fulton, W. Equivariant Cohomology in Algebraic Geometry. (notes from a course) https://people.math.osu.edu/anderson.2804/eilenberg/
5. Libine, M. Lecture Notes on Equivariant Cohomology. Arxiv. [math.AG/0709.3615]