Bradley Ryan PhD

Teacher of Mathematics

Short Resume

About

I am an early career teacher at St Leonard's Catholic School, Durham, England. I completed my PGCE through at Newcastle in June 2025, shortly after finishing my PhD in Pure Mathematics at the University of Leeds in January of the same year. I was supervised by Dr Oleg Chalykh, and co-supervised by Professor Karin Baur. I completed my undergraduate studies at the University of Leeds in July 2020, obtaining an MMath, BSc Mathematics degree.

Qualifications

2025 Secondary PGCE in Mathematics with QTS, University of Newcastle upon Tyne.
Teaching placements at Whitley Bay High School (short) and Ponteland High School (long), alongside the completion of three masters-level modules with a focus on metacognition and oracy:
  • EDU8221 Subject Pedagogy in Practice (83%, PDF)
  • EDU8222 Developing Critical Perspectives on Teaching Thinking Skills (94%, PDF)
  • EDU8223 Curriculum Development Through Enquiry in Practice (90%, PDF)
2025 PhD in Pure Mathematics, University of Leeds.
Thesis: Representations of Quivers and Cherednik Algebras (PDF), supervised by Oleg Chalykh and Karin Baur. Completed the following postgraduate online courses from the MAGIC Consortium:
  • MAGIC008 Lie Groups and Lie Algebras (85%)
  • MAGIC047 Modular Forms (79%)
  • MAGIC064 Algebraic Topology (83%)
  • MAGIC067 Integrable Systems (65%)
2020 MMath, BSc Mathematics, University of Leeds.
Projects: Knot Theory (2020, PDF) and Hyperbolic Geometry (2019, PDF), respectively supervised by James Martin Speight and Derek Harland. Broad background studied with a focus chosen on pure mathematics:
  • MATH5071M Groups, Symmetry and Galois Theory (95%)
  • MATH5113M Advanced Differential Geometry (71%)
  • MATH5195M Advanced Commutative Rings and Algebraic Geometry (94%)
  • MATH5211M Metric Spaces and Functional Analysis (86%)
2016 A-Levels, Temple Moor High School.
Studied Mathematics (A*), Further Mathematics (A), Chemistry (A), History (A), in addition to completing the EPQ (A) with a report entitled Was Mathematics Invented or Discovered?.
    2014 GCSEs, Temple Moor High School.
    Studied Mathematics (A*), English Literature (A*), English Language (A*), Science (A), Additional Science (A), Further Additional Science (A*), History (A*), German (A), Business Studies (A), General Studies (A*).

    University Teaching

    This is an exhaustive list of my university teaching responsibilities. You can also find condensed versions of the lecture notes (each internally dubbed a cheatsheet) for the tutored and marked modules. These are based on notes I made as an undergraduate student, with updates to reflect the then-current versions of each module.

    Academic Year 2023/24

    Academic Year 2022/23

    Academic Year 2021/22

    Academic Year 2020/21

    Tutoring

    As much as I care about understanding and developing new mathematics in a research setting, something which is equally a passion of mine is the process of communicating mathematics with others, especailly if they are not understanding it. After all, what is really the purpose of knowledge if not to share it?

    Online Tutoring

    Since starting my undergraduate studies in September 2016, I have been an online tutor of mathematics. Having led one-on-one tuition with over twenty students, from GCSE to undergraduate level, I got used to communicating both basic and complicated mathematical concepts to people. I am more than happy to provide references to parents/guardians and mature students who want to see if I would be a good tutoring fit for them. The subjects I tutor are A-Level (Further) Mathematics and GCSE Mathematics, from all examination boards. To date, I have not tutored anybody studying mathematics pre-GCSE level but this is something I would like to do.

    Prison Math Project

    I have been involved in the Prison Math Project (homepage) since August 2021, during which time I have had correspondence with a number of inmates who each have a passion for mathematics and want guidance with learning degree-level concepts. This has led me to write what really amounts to lecture notes for them, and then discussing how they find the new material by giving examples and providing exercises. In February 2022, Brady Haran released a podcast with founder Christopher Havens on the YouTube channel Numberphile2 (podcast).

    My main contributions to this venture are to act as a penpal with inmates, and to help design so-called modules for inmates to work through. The (incomplete) resources I have made for this organisation are collated below.

    Research

    My primary research areas of interest are algebra, geometry, topology, representation theory and integrable systems (note that this is certainly not an exhaustive list). During my time as a postgraduate student, the focus has been on representations of Cherednik algebras and quivers. I have, however, studied the interplay between these and the other topics mentioned in the list prior.

    The main goal of my project is to prove a conjecture by Etingof-Gan-Oblomkov (2006), namely that the variety of finite-dimensional irreducible representations of the double affine Hecke algebra of type \(C^\vee C_n\) is isomorphic to a Calogero-Moser space. This isomorphism is known for type \(A_{n-\!1}\) by Oblomkov (2003), so we wish to develop some theory that allows us to adapt this proof for our setting. The next goal is to show that the isomorphism respects Poisson structures, and thence interpret things from the point-of-view of integerable systems.

    Papers

    Presentations

    Conferences

    My old university profile can be found here.