Quantizations and representations.
This is a crash course on basics of (deformation) quantizations and their modules. About five 1-hour lectures.
Schedule:
Aug 28, 10.25-11.25 in KT 801, Lecture 1, notes: I will discuss basics of filtered quantizations and introduce important examples: universal enveloping algebras and algebras of differential operators on smooth affine varieties. If time permits, I'll discuss
a connection with formal quantizations.
Sept 2, 10.25-11.25 in KT 801, Lecture 2, notes: I will discuss formal quantizations and their relation to the filtered ones and then the localization procedure for quantizations (sometimes called the microlocalization).
Sept 4, 10.25-11.25 in KT 801, Lecture 3, notes: I will discuss completions of quantizations, the quantum slice theorem and an application to constructing finite W-algebras.
Sept 16, 10.25-11.25 in KT 801 (note that there's no lectures in week of Sept 8-12), notes: I will start discussion of classification of quantizations concentrating on the symplectic case.
Sept 18, 10.25-11.25 in KT 801, notes: I will define conical symplectic singularities and give some examples. Then I'll discuss their quantizations.
Sept 23, 10.25-11.25 in KT 801, notes: I will talk about modules over quantizations, their good filtrations and associated varieties. We'll also discuss holonomic modules and distinguished good filtrations.
Sept 25, 10.25-11.25 in KT 801, notes: I will talk about the restriction functor for Harish-Chandra modules.
THE END!