Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Modular TemperleyLieb Theory
This dissertation considers the representation theory of TemperleyLieb algebras, TLₙ , along with some related cellular algebras, over positive and mixed characteristic fields. The TemperleyLieb algebras are planar ... 
Ranks of tensors and polynomials, with combinatorial applications
This thesis will consist of three main chapters. It is a standard fact of linear algebra that every matrix with rank k contains a k ⨯ k submatrix with rank k. In Chapter 2 we generalise this fact asymptotically to a class ... 
Modern Methods for Variable Significance Testing
This thesis concerns the ubiquitous statistical problem of variable significance testing. The first chapter contains an account of classical approaches to variable significance testing including different perspectives on ... 
On the Variational Theory of YangMillsHiggs Energies and the Structure of the Singular Set of $\mathbb{Z}$$_{2}$Harmonic Spinors
This dissertation investigates YangMillsHiggs energies and $\mathbb{Z}$$_{2}$harmonic spinors, two classes of objects at the interface between analysis and geometry. In the first part, we present joint work with ...