Brad Ryan


I am a third-year PhD student within the Algebra, Geometry and Integrable Systems Group. Before starting as a postgraduate researcher, I completed my undergraduate course at the University of Leeds. During this time, I did a short investigation into hyperbolic geometry under Dr Derek Harland in 2019, as well as a longer project studying knot theory with Professor Martin Speight in 2020.

Research interests

My current research is focused on understanding the connection between the double affine Hecke algebra of type \(C^\vee C\) and the character variety of a four-punctured Riemann sphere with prescribed eigenvalues (the Calogero-Moser space). Directly related to this is the representation theory of a star-like quiver (or of the corresponding multiplicative preprojective algebra), where the quiver is \(\widetilde{D}_4\) with an additional vertex on one of its legs . A primary aim of my research project is to establish an isomorphism between the Calogero-Moser space and the space of irreducible representations of the so-called spherical subalgebra of the double affine Hecke algebra. Following this, we will then look at things from an integrable systems point-of-view


  • MATH1026 Sets, Sequences and Series, Tutor (2021/22).
  • MATH1060 Introductory Linear Algebra, Tutor (2020/21 and 2022/23).
  • MATH1331 Linear Algebra with Applications, Tutor (2021/22 and 2022/23).
  • MATH1400 Modelling with Differential Equations, Tutor (2022/23).
  • MATH2027 Rings and Polynomials, Module Marker (2022/23).
  • MATH3044 Number Theory, Module Marker (2022/23).

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  • MMath, BSc Mathematics (University of Leeds, 2020).