#### Profile

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

#### Teaching

• 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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#### Qualifications

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