Noncommutative algebra and geometric representation theory

2.3.12 "Differential Operators on affine space" Notes [There is a correction (in red) to the formula for the Poisson bracket I gave in the lecture: thanks to Damien for pointing it out.]

9.3.12 "Holonomic Representations" Notes

16.3.12 "RiemannHilbert Correspondences" Notes
Books on Differential Operators include: Coutinho "A Primer of Algebraic Dmodules" which discusses lots about the Weyl algebra and its ring theory; Hotta, Takeuchi, Tanisaki "Dmodules, Perverse Sheaves, and Representation Theory" which builds up the machinery necessary to prove the BeilinsonBernstein theorem and prove the KazhdanLusztig Conjecture.

23.3.12 "BeilinsonBernstein Theorem" Notes
The statement and proof of a BeilinsonBernstein theorem for general weights can be found in the paper of BackelinKremnizer.

30.3.12 "Symplectic Singularities" Notes

20.4.12 "Symplectic Singularities (ctd)" Notes
There are two good surveys about symplectic singularities: one by Kaledin, the other by Fu.

27.4.12 "Deformations of Symplectic Singularities" Notes

4.5.12 "Deformations of Symplectic Singularities II" Notes

11.5.12 "Deformations of Symplectic Singularities III" Notes
These lectures refer to articles of Namikawa  here and here  and Kaledin (the one above), as well as the book on "Deformation Theory" by Hartshorne.

18.5.12 "Quantizations of Symplectic Varieties and Module Categories" Notes
This lecture uses articles of BezrukavnikovKaledin  here  and KashiwaraRouquier here.

25.5.12 "Waffinity? Quiver varieties and Hilbert schemes" Notes
This lecture uses the above article of KashiwaraRouquier, plus the following: Nakajima, EtingofGinzburg , GordonStafford, GanGinzburg.

1.6.12 "Geometric Category O; Hypertoric Varieties" Notes
This lecture refers to the following: BellamyKuwabara and BradenLicataProudfootWebster.
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