This volume contains the proceedings of the virtual AMS Special Session on Equivariant Cohomology, held March 19-20, 2022. Equivariant topology is the algebraic topology of spaces with symmetries. At the meeting, ""equivariant cohomology"" was broadly interpreted to include related topics in equivariant topology and geometry such as Bredon cohomology, equivariant cobordism, GKM (Goresky, Kottwitz, and MacPherson) theory, equivariant $K$-theory, symplectic geometry, and equivariant Schubert calculus. This volume offers a view of the exciting progress made in these fields in the last twenty years. Several of the articles are surveys suitable for a general audience of topologists and geometers. To be broadly accessible, all the authors were instructed to make their presentations somewhat expository. This collection should be of interest and useful to graduate students and researchers alike.
Noe Barcenas, A survey of computations of Bredon cohomology
Jack Carlisle, Cobordism of $G$-manifolds
Jeffrey D. Carlson, The cohomology of homogeneous spaces in historical
context
Chi-Kwong Fok, A stroll in equivariant $K$-theory
Matthias Franz, The Chang-Skjelbred lemma and generalizations
Oliver Goertsches, Panagiotis Konstantis and Leopold Zoller, Low-dimensional
GKM theory
Rebecca Goldin, On positivity for the Peterson variety
Chen He, Localization of equivariant cohomology rings of real and oriented
Grassmannians
Matvei Libine, Localization of integrals of equivariant forms for non-compact
group actions
Andres Pedroza, Induced Hamiltonian function on the symplectic one-point
blowup
Loring W. Tu, Gysin formulas and equivariant cohomology
Julianna Tymoczko, A concise introduction to GKM theory, 25 years on
Loring W. Tu, Tufts University, Medford, MA
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