University of St Andrews University of St Andrews

MT5821: Advanced Combinatorics


PhD studentship in Auckland
From Gabriel Verret:
"I am advertising a 3-year Ph.D. scholarship at
the University of Auckland, to work with me on a
project in finite groups or algebraic graph theory.
Ideally, I am looking for a student with a Master's
degree or equivalent, with some basic research
experience in this area, and who would be ready
to start some time in 2019. The stipend is
27600 NZD/year (plus domestic fees), with an annual
cost-of-living adjustment. This is standard for a
University of Auckland doctoral scholarship and is
enough to cover basic living expenses."
This year's Advanced Combinatorics module would be
good background for this. Email him, or talk to me,
if you are interested.

The module

The module will run in Semester 2 (28 January to 25 April), with Spring break from 18 March to 29 March.

The course will this year cover the third of the approved syllabuses: Finite Geometry. The module descriptor says,

Projective and polar spaces: geometry of vector spaces, combinatorics of projective planes, sesquilinear and quadratic forms and their classification, diagram geometry, classical groups.
You will also be introduced to root systems (one of the most pervasive ideas in mathematics, related to the classification of Lie algebras, singularity theory, cluster algebras, etc. – though we will not cover these topics!).

Timetable

Lectures will be in Room 1A on Mondays (odd weeks), Wednesdays and Fridays 12:00-13:00.

Two tutorial hours have been scheduled. These are Mondays 15:00-16:00 and Tuesdays 11:00-12:00 (not week 1), both in Room 3B. The reason for two tutorials was that, because of a clash, some people were not able to make the Monday tutorial, and so an alternative was scheduled. There is no need to attend both! Please let me know as soon as possible if one or both of these times is not possible for you.

Lecture notes

Lecture notes will be posted here. If you want a preliminary look, you can find the 2015-2016 web page here.

Problems and solutions

Weekly problems, and occasional revision problems, will also be posted here. The assessment is 100% exam, but it is recommended that you try your hand at some of the problems. Work handed in will be returned to you with comments as quickly as possible.

Exam resources

There is a sample exam paper and the 2016 exam paper available. I do not have solutions to these papers, but I will be happy to go over your attempts at either or both with you before the exam.

Other resources

You can find here the slides of a talk on The ADE affair, one of the most pervasive themes in mathematics, which will be touched on in the lectures.

Peter J. Cameron
Room 317, Mathematical Institute
pjc20@st-andrews.ac.uk
21 January 2019