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 "Riemann-Hilbert Correspondences" Notes
Books on Differential Operators include: Coutinho "A Primer of Algebraic D-modules" which discusses lots about the Weyl algebra and its ring theory; Hotta, Takeuchi, Tanisaki "D-modules, Perverse Sheaves, and Representation Theory" which builds up the machinery necessary to prove the Beilinson-Bernstein theorem and prove the Kazhdan-Lusztig Conjecture.
• 23.3.12 "Beilinson-Bernstein Theorem" Notes
The statement and proof of a Beilinson-Bernstein theorem for general weights can be found in the paper of Backelin-Kremnizer.
• 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 Bezrukavnikov-Kaledin - here - and Kashiwara-Rouquier here.
• 25.5.12 "W-affinity? Quiver varieties and Hilbert schemes" Notes
This lecture uses the above article of Kashiwara-Rouquier, plus the following: Nakajima, Etingof-Ginzburg , Gordon-Stafford, Gan-Ginzburg.
• 1.6.12 "Geometric Category O; Hypertoric Varieties" Notes
This lecture refers to the following: Bellamy-Kuwabara and Braden-Licata-Proudfoot-Webster.

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