## University of Sydney Algebra Seminar

# Eric Friedlander (University of Southern California)

## Friday 30th November, 12:05-12:55pm, Carslaw 173

### Invariants for representations (following Quillen's equivariant cohomology)

In back-to-back papers in Annals 1971, Dan Quillen formulated equivariant cohomology theory to give an explicit description of the spectrum of the cohomology of a finite group. Quillen's introduction of algebraic geometry to group cohomology has led to support varieties of modular representations and structural results about the stable module category for finite groups. We describe how cohomology has somewhat receded from the scene, how methods evolving from Quillen's work apply to other module categories, how support varieties admit refinements, and how algebraic vector bundles arise from special classes of modules. This talk will touch upon collaborations over the years with Brian Parshall, Andrei Suslin, Chris Bendel, Jon Carlson, and especially Julia Pevtsova.