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

Mortality linked derivatives and their pricing
(The University of Edinburgh, 20171130)This thesis addresses the absence of explicit pricing formulae and the complexity of proposed models (incomplete markets framework) in the area of mortality risk management requiring the application of advanced techniques ... 
Combinatorics of Gaudin systems: cactus groups and the RSK algorithm
(The University of Edinburgh, 20161129)This thesis explores connections between the Gaudin Hamiltonians in type A and the combinatorics of tableaux. The cactus group acts on standard tableaux via the Schützenberger involution. We show in this thesis that the ... 
Double Hilbert transforms along surfaces in the Heisenberg group
(The University of Edinburgh, 20170710)We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹, that is operator f ↦ Hφ f (x) := p.v.∫∣s∣,∣t∣≤1 f (x ∙ (s, t ,φ(s, t ))¹) ds/s dt/t, ... 
Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter
(The University of Edinburgh, 20161129)We are interested in rigorous asymptotic results pertaining to three different differential equations which lie in the Heun class (see [1] §31). The Heun class contains those ordinary linear secondorder differential ... 
Deformation theory of a birationally commutative surface of GelfandKirillov dimension 4
(The University of Edinburgh, 20161129)Let K be the field of complex numbers. In this thesis we construct new examples of noncommutative surfaces of GKdimension 4 using the language of formal and infinitesimal deformations as introduced by Gerstenhaber. Our ... 
On geometric inequalities related to fractional integration
(The University of Edinburgh, 20161129)The first part of this thesis establishes a series of geometric ineqalities related to fractional integration in some geometric settings, including bilinear and multilinear forms. In the second part of this thesis, we ... 
Use of proof planning in normalisation
(The University of Edinburgh, 1995) 
Some aspects of the mathematical modelling of fixed bed chemical reactors
(The University of Edinburgh, 1975) 
New stability conditions on surfaces and new Castelnuovotype inequalities for curves on completeintersection surfaces
(The University of Edinburgh, 20160629)Let X be a smooth complex projective variety. In 2002, [Bri07] defined a notion of stability for the objects in Db(X), the bounded derived category of coherent sheaves on X, which generalized the notion of slope stability ... 
Sketch and project: randomized iterative methods for linear systems and inverting matrices
(The University of Edinburgh, 20160629)Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ... 
Solitary waves in focussing and defocussing nonlinear, nonlocal optical media
(The University of Edinburgh, 20160629)Nonlinear, nonlocal optical media has emerged as an ideal setting for experimentally observing and studying spatial optical solitary waves which otherwise cannot occur in Kerr media. Of particular interest is the eventual ... 
Stochastic PDEs with extremal properties
(The University of Edinburgh, 20160629)We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of ... 
Application of Bridgeland stability to the geometry of abelian surfaces
(The University of Edinburgh, 20160629)A key property of projective varieties is the very ampleness of line bundles as this provides embeddings into projective space and allows us to express the variety in equational terms. In this thesis we study the general ... 
Extended stochastic dynamics: theory, algorithms, and applications in multiscale modelling and data science
(The University of Edinburgh, 20160629)This thesis addresses the sampling problem in a highdimensional space, i.e., the computation of averages with respect to a defined probability density that is a function of many variables. Such sampling problems arise ... 
Firstorder numerical schemes for stochastic differential equations using coupling
(The University of Edinburgh, 20160629)We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion ... 
Construction of Seifert surfaces by differential geometry
(The University of Edinburgh, 20160629)A Seifert surface for a knot in ℝ³ is a compact orientable surface whose boundary is the knot. Seifert surfaces are not unique. In 1934 Herbert Seifert provided a construction of such a surface known as the Seifert Algorithm, ... 
Hyperarithmetical properties of relations on abelian pgroups and orderings
(The University of Edinburgh, 1992) 
Water entry and related problems
(The University of Edinburgh, 1972) 
Homogeneity in supergravity
(The University of Edinburgh, 20160629)This thesis is divided into three main parts. In the first of these (comprising chapters 1 and 2) we present the physical context of the research and cover the basic geometric background we will need to use throughout ... 
Codensity, compactness and ultrafilters
(The University of Edinburgh, 20160629)Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff ...