Bradley Ryan

Profile

I am a fourth-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, followed by a longer project studying knot theory with Professor Martin Speight in 2020.

Website

My personal home page includes more details about my research and teaching.

Research interests

My current research is focused on understanding the connection between the double affine Hecke algebra of type \(C^\vee C_n\) and the character variety of a four-punctured Riemann sphere with prescribed eigenvalues, the so-callled Calogero-Moser space. A primary aim of my research project is to establish an isomorphism between the Calogero-Moser space and the variety of irreducible representations of the double affine Hecke algebra. Following this, we wish to look at things from an integrable systems point-of-view. In particular, we aim to show that the isomorphism respects Poisson structures; this is analogous to the type \(A_{n-1}\) situation studied by Oblomkov.

Current Teaching

• MATH1025 Number Systems, Tutor.
• MATH1026 Sets, Sequences and Series, Tutor.
• MATH1225 Introduction to Geometry, Tutor.
• MATH2017 Real Analysis, Marker.
• MATH2027 Rings and Polynomials, Marker.

<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>

<style>h4{text-transform: capitalize;} ul.list-facts strong{text-transform: capitalize;} .back-top{margin-top: 30px;}</style>

Qualifications

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