Mathematics thesis and dissertation collection
This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.
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Recent Submissions

Multijoints and multilinear duality
(The University of Edinburgh, 20220525)The joints problem is related to geometric questions at the heart of harmonic analysis. In three dimensions, a joint is a point of intersection of three lines that do not lie within a common plane. Given a collection of ... 
Quantum symmetric pairs in topological field theory
(The University of Edinburgh, 20191128)[No Deposit Agreement] 
Factorisation homology and skein categories of surfaces
(The University of Edinburgh, 20191128)[No Deposit Agreement] 
Fano varieties: positivity, Kstability and more
(The University of Edinburgh, 20220411)This thesis is about Fano varieties and their properties. We will determine the Kstability of certain singular del Pezzo surfaces and smooth Fano 3folds, the existence of cylinders in singular del Pezzo surfaces, and ... 
Iterative methods for solving stochastic optimal control problems
(The University of Edinburgh, 20220404)Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Therefore, most of the time, they have to be solved numerically. In this ... 
Regularized interior point methods for convex programming
(The University of Edinburgh, 20220323)Interior point methods (IPMs) constitute one of the most important classes of optimization methods, due to their unparalleled robustness, as well as their generality. It is well known that a very large class of convex ... 
Bayesian methods for biomarker evaluation and disease diagnosis
(The University of Edinburgh, 20220322)Accurate diagnosis of disease is of fundamental importance in medical research and clinical practice. For such reason, the role that diagnostic testing and screening play is undeniable. The major goal of a diagnostic ... 
Methods for the analysis of oscillatory integrals and BochnerRiesz operators
(The University of Edinburgh, 20220321)For a smooth surface Γ of arbitrary codimension, one can consider the Lp mapping properties of the BochnerRiesz multiplier m(ζ) = dist(ζ,Γ)^α φ(ζ), where α > 0 and φ is an appropriate smooth cutoff function. Even for ... 
Constructing and classifying fivedimensional black holes using integrability
(The University of Edinburgh, 20220317)In this thesis we look at the problem of nding and classifying stationary and biaxisymmetric solutions in vedimensional theories of gravity, using particular hidden symmetries. We consider three theories: the electrostatic ... 
Statistical modelling of environmental extremes
(The University of Edinburgh, 20220316)This thesis is concerned with the development of theory and statistical methodologies that may be used to analyse environmental extremes. As extreme environmental events are often associated with large economic costs and ... 
Mixedmode oscillations in singularly perturbed threetimescale systems
(The University of Edinburgh, 20220222)In this work, we are concerned with the dynamics of threedimensional, threetimescale systems of ordinary differential equations. Systems with two timescales have been extensively studied, while the theory of systems ... 
Randomly assembled cyclic multiblock ADMM: a fast method for largescale linearly constrained quadratic optimization
(The University of Edinburgh, 20220222)This work is motivated by a simple question: how to find a relatively good solution to a very large optimization problem in a limited amount of time. We consider the linearly constrained convex minimization model with ... 
Bayesian inverse problems
(The University of Edinburgh, 20211127)We consider linear, mildly illposed inverse problems in separable Hilbert spaces under Gaussian noise, whose covariance operator is not identity (i.e. it is not a white noise problem), and use the Bayesian approach to ... 
Thermal effects on nonlinear optical beam propagation in nematic liquid crystals
(The University of Edinburgh, 20211127)This thesis examines in detail the study of nonlinear wave phenomena arising in different contexts in applied nonlinear optics. In particular, it explores the intricate nonlinear interplay between light and matter using ... 
Low regularity wellposedness of the modified and the generalized Kortewegde Vries equations
(The University of Edinburgh, 20211127)In this thesis, we study the wellposedness of the modified and generalized Kortewegde Vries equations on the onedimensional torus. We first consider the complexvalued modified Kortewegde Vries equation (mKdV). We ... 
Extreme precision and extreme complexity: source modelling and data analysis development for the laser interferometer space antenna
(The University of Edinburgh, 20211127)Gravitational wave (GW) observations made with the LIGO and Virgo interferometers are transforming our understanding of the astrophysics of stellar origin compact objects (CO). The planned Laser Interferometer Space Antennae ... 
A ddimensional analyst's Travelling Salesman theorem for arbitrary sets in Euclidean space
(The University of Edinburgh, 20211127)In this thesis, we discuss recent progress on higher dimensional analogues to the Analyst’s Travelling Salesman Theorem (TST) of Peter Jones. The TST characterizes subsets of rectifiable curves in the plane, via a multiscale ... 
Beyond Lorentzian symmetry
(The University of Edinburgh, 20211127)This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the ... 
Multilinear geometric inequalities
(The University of Edinburgh, 20211127)In this thesis we explore a multilinear duality principle of Carbery–Hänninen–Valdimarsson for multilinear geometric inequalities arising in Harmonic Analysis. In Chapter 2, we give a brief survey of how this theory ... 
Efficient algorithms for solving pmedian problems with radius constraints; and, Its application to clustering with feature selection
(The University of Edinburgh, 20210731)Facility location problems aim to identify where to locate facilities to satisfy the demand of a given set of customers. A location for a facility is selected by minimising the total supply cost of the demand to the ...