Assorted notes

Expositions and reading groups

An exposition on algebraic \(K_0\) and \(K_1\).

A brief introduction to stacks via toric geometry and moduli of elliptic curves.

My class paper on the etale fundamental group for the Fall 2015 course Math 215A Algebraic topology at UC Berkeley. Also some notes on de Rham's theorem and higher \(K\)-theory for the same course.

Another class paper on Abelian varieties and the Hodge conjecture for the Fall 2015 course Math 256A Algebraic geometry at UC Berkeley.

Some fun notes on the Klein quartic made in winter 2015. See the very last section for something mildly original.

A lighthearted rant on the Weyl reducibility theorem. Dedicated to Jeremy Meza.

Some more \(K\)-theory discussing the Quillen-Suslin theorem.

One more class paper on cluster structures in Lie theory and the semicanonical basis for the Spring 2016 Math 261B Lie groups course.

Note that most of my recent informal notes (from January 2016 onwards) are posted on my blog instead of here.

Course notes

Notes on elementary group and ring theory, based on the lecture course given by Inna Capdeboscq at Warwick in Spring 2013.

A excerpt on regular perturbation theory from a revision guide for the MA254 Theory of ODEs course at Warwick taught by Christoph Ortner also in Spring 2013.

Course notes for an introduction to manifolds, based on the lecture course given by Alix Deruelle at Warwick in Autumn 2013.

Notes for the final five weeks (i.e. post-'singular isomorphic to simplicial' homology) of the algebraic topology course taught at Warwick by Saul Schleimer in Spring 2014.

Notes for Alex Bartel's Spring 2015 representation theory course.

Disclaimer: These all contain my preferences (and prejudices) concerning notation and, in places, the actual approach taken so will not absolutely resemble the courses given in respective years.

Grad school

Since going through the application process (sucessfully!) to American grad schools I have received many questions about it. Here is a brief guide to the process that I wrote in summer 2015 primarily for University of Warwick students (mostly regarding the geography). I sat the GRE mathematics subject test in September 2014; these are my revision notes. Notice the amusing similarities to my revision notes used for teaching STEP.

I passed my prelim exam at UC Berkeley in August 2015. Here are some summary notes and solutions to past problems.

I passed my qualifying exam at UC Berkeley in November 2016. Here is my syllabus and transcript.

Got to get something done today
Give accomplishment a shot
Might not have a full palette to use
But I'm gonna paint with the colors I've got
- Bruce Hornsby.