Mathematics
This page contains links to various notes that I have written. These are typically calculations and solutions to exercises. I must stress that these are very rough in nature. These documents have in no way been peer reviewed and are in general an expression of my own understanding of a subject. I do not claim that they will always be completely accurate or referenced correctly. They are merely here as information for anyone who may want to use them.
If you find any mistakes in any of these files then please do not hesitate to contact me and I will gladly correct them. With any luck, I will also learn something in the process.
Posters
- Unipotent Supports of Finite Reductive Groups. This poster was made for the Workshop on Representation Theory, which was held at the University of Birmingham (15th-18th June 2011).
Notes From Courses
- An Introduction to the Representation Theory of Finite Groups. These notes are taken from a summer school held at RWTH Aachen University in September 2010. The notes cover the three courses given by Gerhard Hiss, Radha Kessar and Burkhard Külshammer.
Calculations
- Determining the roots and coroots of the odd rank special orthogonal group.
- Determining the structure of centralisers of semisimple elements in the algebraic group SO(5,K).
- An example of calculating Lusztig's truncated induction in the Symmetric group on 4 letters.
- An example of calculating Lusztig's families for the Weyl group of type B_3.
GAP Programs
- lsymbols(v3) and lsymbols(v4). This is a program designed to run in GAP 3 together with the package CHEVIE (either the stable version v3 or the development version v4 maintained by Jean Michel). It implements the combinatorial symbols of Lusztig to calculate families of complex irreducible characters of the Weyl group. Note: Lusztig's symbols have now been implemented in the development version of CHEVIE (specifically see Chapter 94 of the manual). However this program can still be used to quickly compute the families of irreducible characters.
LaTeX Examples
- This zip file contains examples of LaTeX documents as a reference for project students trying to write their final year report.
Lecture Notes (York) - Years 06/07 and 07/08
- Calculus of Variations. Taught by Prof. Arnold Arthurs.
- Fluid Mechanics. Taught by Prof. Vladimir Vladimirov.
- Formal Languages and Automata. Taught by Dr. Victoria Gould.
- Number Theory. Taught by Prof. Sanju Velani.
- Further Number Theory. Taught by Prof. Sanju Velani.
- Lie Algebras. Taught by Prof. Maxim Nazarov.
- Further Quantum Mechanics. Taught by Dr. Chris Fewster.
- Representation Theory of the Symmetric Group. Taught by Prof. Maxim Nazarov.
- Riemannian Geometry. Taught by Dr. Ian McIntosh.
- Semigroup Theory. Taught by Dr. Victoria Gould.