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.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Recent Submissions

Fano threefolds and algebraic families of surfaces of Kodaira dimension zero
(The University of Edinburgh, 20101124)The thesis consists of four chapters. First chapter is introductory. In Chapter 2, we recall some basic facts from the singularity theory of algebraic varieties (see Section 2.2) and the theory of minimal models (see ... 
Inertiagravity wave generation: a WKB approach
(The University of Edinburgh, 20110628)The dynamics of the atmosphere and ocean are dominated by slowly evolving, largescale motions. However, fast, smallscale motions in the form of inertiagravity waves are ubiquitous. These waves are of great importance ... 
Moduli of bundles on local surfaces and threefolds
(The University of Edinburgh, 20101124)In this thesis we study the moduli of holomorphic vector bundles over a noncompact complex space X, which will mainly be of dimension 2 or 3 and which contains a distinguished rational curve ℓ ⊂ X. We will consider the ... 
Parabolic boundary value problems with rough coefficients
(The University of Edinburgh, 20181129)This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has ... 
Crepant resolution conjecture for DonaldsonThomas invariants via wallcrossing
(The University of Edinburgh, 20181129)Let Y be a smooth complex projective Calabi{Yau threefold. DonaldsonThomas invariants [Tho00] are integer invariants that virtually enumerate curves on Y. They are organised in a generating series DT(Y) that is interesting ... 
Wellposedness of the onedimensional derivative nonlinear Schrödinger equation
(The University of Edinburgh, 20181129)This thesis is concerned with the wellposedness of the onedimensional derivative nonlinear Schrodinger equation (DNLS). In particular, we study the initialvalue problem associated to DNLS with lowregularity initial ... 
Many server queueing models with heterogeneous servers and parameter uncertainty with customer contact centre applications
(The University of Edinburgh, 20181129)In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the HalfinWhitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates ... 
Geometry of the cubic surfaces: with special reference to the 27 straight lines on the surface
(The University of Edinburgh, 1913) 
A correspondence between null and ordinary geodesics, its properties and Straneo's unified theory
(The University of Edinburgh, 1933) 
Contributions to the theory of hypergeometric functions and other papers
(The University of Edinburgh, 1940) 
Singularities of noncommutative surfaces
(The University of Edinburgh, 20181129)The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also be singular, in the sense that they have infinite ... 
On knormality and regularity of normal projective toric varieties
(The University of Edinburgh, 20180702)We study the relationship between geometric properties of toric varieties and combinatorial properties of the corresponding lattice polytopes. In particular, we give a bound for a very ample lattice polytope to be knormal. ... 
Bridgeland stability conditions, stability of the restricted bundle, BrillNoether theory and Mukai's program
(The University of Edinburgh, 20181129)In [Bri07], Bridgeland introduced the notion of stability conditions on the bounded derived category D(X) of coherent sheaves on an algebraic variety X. This topic is originally inspired by concepts in string theory and ... 
Stochastic, distributed and federated optimization for machine learning
(The University of Edinburgh, 20171130)We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that ... 
Design of reliable aerospace system architecture
(The University of Edinburgh, 20181129)Reliability and redundancy of safetycritical network systems is a paramount issue in system engineering. Be it in evaluating existing network systems or solving optimization problems for designing network systems, it ... 
Statistical methods for the testing and estimation of linear dependence structures on paired highdimensional data: application to genomic data
(The University of Edinburgh, 20180702)This thesis provides novel methodology for statistical analysis of paired highdimensional genomic data, with the aimto identify gene interactions specific to each group of samples as well as the gene connections that ... 
Heuristic methods for solving two discrete optimization problems
(The University of Edinburgh, 20180702)In this thesis we study two discrete optimization problems: Traffic Light Synchronization and Location with Customers Orderings. A widely used approach to solve the synchronization of traffic lights on transport networks ... 
Two geometric inequalities in harmonic analysis
(The University of Edinburgh, 2010)We study two geometric inequalities in harmonic analysis. 
Theorems in the tensor calculus, with applications to relativity
(The University of Edinburgh, 1932) 
The use of proof plans in tactic synthesis
(The University of Edinburgh, 1993)We undertake a programme of tactic synthesis. We first formalize the notion of a tactic as a rewrite rule, then give a correctness criterion for this by means of a reflection mechanism in the constructive type theory ...