Theses  Pure Mathematics and Mathematical Statistics: Recent submissions
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
A simply laced Dynkin diagram gives rise to a family of curves over Q and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven ... 
On Gaussian multiplicative chaos and conformal field theory
This thesis is concerned with conformally invariant stochastic processes in two dimensions and their applications to conformal field theory (CFT). The main probabilistic objects are the Gaussian free field (GFF) and the ... 
Homogenization of Random Media: Random Walks, Diffusions and Stochastic Interface Models
This thesis concerns homogenization results, in particular scaling limits and heat kernel estimates, for random processes moving in random environments and for stochastic interface models. The first chapter will survey ... 
A Tool for Producing Verified, Explainable Proofs
Mathematicians are reluctant to use interactive theorem provers. In this thesis I argue that this is because proof assistants don't emphasise explanations of proofs; and that in order to produce good explanations, the ...