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

Properties and advances of probabilistic and statistical algorithms with applications in finance
(The University of Edinburgh, 20190701)This thesis is concerned with the construction and enhancement of algorithms involving probability and statistics. The main motivation for these are problems that appear in finance and more generally in applied science. ... 
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 ... 
Mathieu functions
(The University of Edinburgh, 1936)This thesis is divided into two parts. In the first part, I have studied the properties of certain functions of the confluent hypergeometric types, viz. Functions of Mathieu, Whittaker, Weber and Bateman. The development ... 
On the theory of matrices with elements in the Clebsch Aronhold symbolic calculus
(The University of Edinburgh, 1949)In the theory of invariant matrices and in the classical invariant theory there arise a considerable number of rather surprising isonorphisms relating to symmetric functions of the latent roots and to the theory of ... 
Invariant theory of the differential geometry of contact transformations
(The University of Edinburgh, 1937)Corresponding to the group of all analytic transformations there is a differential geometry of what is called the affinely connected space, which is a generalization of the ordinary affine geometry in the sense of Klein. ... 
Some mathematical problems to the factorial analysis of human ability
(The University of Edinburgh, 1940)1st Paper (1936): "Some Mathematical Remarks concerning Boundary Conditions in the Factorial Analysis of Ability" (Psychometrika, vol. 1, 165 174)  2nd Paper (1937): "On an Upper Limit for the Latent Roots of a ... 
On the test of a hypothesis concerning two independent frequency distributions
(The University of Edinburgh, 1948)One of the chief uses of statistical analysis of given samples, which are of course assumed to be representative in the statistical sense, is to draw correct inferences regarding their populations. 
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) 
Researches in nonassociative algebra
(The University of Edinburgh, 1941)I have frequently been asked by biologists for mathematical help in connection with their problems. I was working on one such problem when an algebraist, observing my work without knowing what it was about, remarked ... 
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 ...