Notes

Math 843: Representation Theory Lecture Notes

Hensel’s lemma for noncommutative rings

Geometric Representation Theory in Positive Characteristic

On an identity of Hochschild:
A proof of an identity of Hochschild

Quantization of symplectic varieties in positive characteristic. This is my topic exam from 2020 at the University of Chicago. It contains an explicit formula for the first-order Frobenius-split quantization constructed by Bezrukavnikov and Kaledin.

D-modules

From a talk in Kazhdan-Lusztig conjecture seminar, Winter 2020:
Regular holonomic D-modules and equivariant Beilinson-Bernstein

From a series of two lectures I gave on D-modules in the Fall of 2019:
Introduction to D-modules I
Introduction to D-modules II

Half Haunted

I am writing a series of expository blog posts with Catherine Ray on 1/2’s that appear in mathematics, such as in the Duflo and HKR isomorphisms.

Relating the 1/2’s in Duflo and Harish-Chandra
The 1/2 in Harish-Chandra via the Fourier Transform
Note that these are hosted on Catherine’s website.

Other

Some notes on representations of the unitary group