Lecture Notes
Lecture Notes (as lecturer)
Notes that I created for various lecture courses that I gave.
Algebraic Number Theory (updated Jan 2023).
Introduction to Proofs (updated Sep 2023)
1st Year PhD Report
This is the report I wrote for my first year of PhD. It gives a brief background to K3 surfaces and Picard groups. This is followed by a discussion on different methods to find the Picard rank of K3 surfaces, before applying the theory to a specific family of K3 surfaces.
4th Year Project (Master Project)
This is the essay I did during my fourth year MMath degree at Warwick. It is on binary quadratic forms, Gauss composition and Bhargava's cubes. It starts with a quick recapitulation on Gauss composition before covering in details, with examples, Bhargava's cubes as discussed by Manjul Bhargava's 2004 paper on Higher Composition Laws I.
Lectures and Study Groups Notes (as student)
These are various lectures and study groups notes that I have typed up while attending courses at the University of Warwick (or conferences elsewhere). They have not been thoroughly checked and might still contained typos and errors. Feel free to download them for your personal use but do not solely rely on them for your exams, especially if the notes are not from your year; courses can (and will) change from year to year. Please email me any correction that needs to be made.
Due to popular request, I am also including both a TeX and LyX file of most set of completed notes. If you have never used Tex or want to learn to use TeX with a more WYSIWYM I strongly encourage you to check out Lyx.
Algebraic Geometry (from the 2011-2012 course): TeX, LyX.
Algebraic Geometry 2 (from the 2014-2015 course).
Algebraic Groups (Study Group Autumn 2014).
Algebraic Number Theory (from the 2010-2011 course): TeX, LyX.
Algebraic Number Theory 2 (from the 2014-2015 TCC course).
Commutative Algebra (from the 2011-2012 course, references to commutative algebra in Ring Theory refer to these notes): TeX, LyX.
Commutative Algebra II (from the 2012-2013 course): TeX.
Euler Systems (Study Group Summer 2015).
Galois Representations (Study group Autumn 2014).
Graduate Algebra (from the 2012-2013 course): TeX, LyX.
Introduction to Hodge Theory and K3 surfaces (based on a Master Class in Strasbourg 2013).
Intersection Theory (Study Group Autumn 2014).
Local Fields (from the TCC 2013-2014 course): TeX, LyX.
Modular Curves (from the TCC 2013-2014 course): TeX, LyX.
Modular Representation (Study Group Summer 2015).
Presentation of Groups (from the 2012-2013 course): TeX, LyX.
Quadratic Forms (from the 2011-2012 course): TeX, LyX.
Representation Theory (from the 2013-2014 course): TeX, LyX.
Ring Theory (from the 2012-2013 course): TeX, LyX.
Schottky Groups and Mumford Curves (Study Group Summer 2014).