Teaching 

Matroid Theory (Taught Course Center - Bath/Bristol/Imperial/Oxford/Warwick/Swansea)

In the autumn term of 2023 I will be teaching a lecture series on Matroid Theory for graduate students as part of the Taught Course Centre (TCC). 

Lectures will take place 10:00 - 12:00 on Thursdays, commencing on 12th October. 

The course will consist of 8 lectures of two hours each. There will be no lecture on 2nd November, hence we will conclude on Thursday 7th December. 

Prerequisites: A knowledge of Linear Algebra, comparable to a 1st or 2nd year Linear Algebra module. (Some graph theory would be useful but not required)

Registration is required and closes on 2nd October. 

Content:

Here is a list of topics I hope to cover during the course. The majority of the structure and content follows Oxley's book on Matroid Theory (https://academic.oup.com/book/34846 )

• Introduction - Basic definitions, and introduction to a selection of axiom systems (Independence, Circuits, Bases), in particular being motivated from graphs and matrices. Basic examples and connections between definitions. 

  • Lecture 1 

  • Lecture 1 (Live Notes)

• Rank and Closure operations, Lattice of Flats and classification in terms of geometric lattices.

  • Lecture 2

  • Lecture 2 (Live Notes)

  • Lecture 3 (Live Notes)

• Duality, specifically for representable and graphic matroids, Whitney's 2-isomorphism theorem.

  • Lecture 3

  • Lecture 4

  • Lecture 4 (Live Notes)

• Minors: Deletion & Contraction. Classes of minor-closed matroids. 

  • Lecture 5 

  • Lecture 5 (Live Notes)

• Geometric representations and the Greedy algorithm. 

  • Lecture 6

  • Lecture 6 (Live Notes)

• Geometric objects associated to matroids (Polytope & Bergman Fan)

  • Lecture 7

  • Lecture 7 (Live Notes)

• Tutte and Characteristic polynomials, Rota-Welsh conjecture and recent developments. 

  • Lecture 8

  • Lecture 8 (Live Notes)

I will try to be as thorough as possible in such a broad subject, meaning I will not include all proofs but only those that I find enlightening and which I think aid intuition. 

Depending on how the lectures go, there may be time to discuss other areas where matroids have applications. Please let me know if there is anything you would specifically like to hear about. 

Lecture Notes: I will upload lecture notes here as we proceed through the course. I hope that they will be typed but if not they will be my hand written ones. 

Exercises: There will be several exercise sheets to accompany the lectures. 

Tutorials 

In spring 2023 I lead two 1st year tutroial groups for the Linear Algebra module. The groups consisted of 10-14 students and I was responsoble for planning and leading sessions every other week. I was also required to mark the assignments in the weeks inbetween. I aimed to use interactive activities during my sessions enableing me to monitor engagement, understanding and progress. 

AFHEA

During my PhD I was a teaching assistant for several undergraduate modules. The role included planning and running Examples/Exercise classes and helping with the marking load for the assignments/homework. In November 2021 I was recognised as an Associate Fellow of the Higher Education Academy (AFHEA).