The Geometric Representation Theory Seminar is a learning seminar in the 2017-18 academic year, run by Justin Hilburn. The Goal of this seminar is to learn about, perverse sheaves, quiver varieties, canonical bases, KLR algebras and categorical representations of Lie algebras. We are starting on perverse sheaves in Summer 2017.
The seminar does not currently have a regular meeting time.
A list of useful references is given by:
On Perverse Sheaves
Our primary reference is the following, we are currently going through all exercises contained therein:
Further References
- Nicolaescu, The Derived Category of Sheaves and the Poincare-Verdier duality (For background)
- MacPherson, Intersection Homology and Perverse Sheaves (For more on intersection homology, and topology)
- Ginzburg, Characteristic varieties and vanishing cycles
- Schapira, A short review on microlocal sheaf theory (For microlocal Thoery)
- Braden, Hyperbolic localization of intersection cohomology
- Goresky, Kottwitz, and MacPherson Equivariant cohomology, Koszul duality,
and the localization theorem
- Liu, and Zheng, Enhanced adic formalism and perverse t-structures for higher Artin stacks (In the closely related setting of etale sheaves this paper describes perverse sheaves for (Higher) Artin stacks, ideally it should be possible to work out the analogue for perverse sheaves on higher complex analytic stacks.)
Quiver Varieties
Canonical Bases of Quantum Groups
Category O for Quiver Varieties
KLR algebras and Categorical Lie algebra Representations