Department of Pure Mathematics and Mathematical Statistics (DPMMS)
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Geometric Functional Data Analysis
(20191026)In this thesis, we introduce a comprehensive framework for the analysis of statistical samples that are functional data with nontrivial geometry. Geometry can interplay with functional data in different forms. The most ... 
Inferring differences between networks using Bayesian exponential random graph models
(20191026)The goal of many neuroimaging studies is to better understand how the functional connectivity structure of the brain changes with a given phenotype such as age. Functional connectivity can be characterised as a network, ... 
Level raising for automorphic representations of GL(2n)
(20190518)To each regular algebraic, conjugate selfdual, cuspidal automorphic representation $\Pi$ of $\mathrm{GL}(N)$ over a CM number field $E$ (or, more generally, to a regular algebraic isobaric sum of conjugate selfdual, ... 
Ricciflat deformations of orbifolds and asymptotically locally Euclidean manifolds
(20190719)In this thesis we study Ricciflat deformations of Ricciflat Kähler metrics on compact orbifolds and asymptotically locally Euclidean(ALE) manifolds. In both cases we also study the moduli space of Ricciflat structures. ...