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

Gradings on the Brauer algebras and double affine BMW algebras
(The University of Edinburgh, 20210731)In this thesis we study algebras that appear in di erent generalisations of the wellknown SchurWeyl duality. This classical result gives a remarkable connection between the irreducible finitedimensional representations ... 
On the McKeanVlasov dynamics with or without common noise
(The University of Edinburgh, 20210731)McKeanVlasov stochastic differential equations may arise from a probabilistic interpretation of certain nonlinear PDEs or as the limiting behaviour of mean field particle systems (those whose interactions are through ... 
Noetherianity of idealizers in skew extensions
(The University of Edinburgh, 20201130)Given a right ideal I in a ring R, the idealizer of I in R is the largest subring of R in which I becomes a twosided ideal. These rings are of interest since they often give examples of rings with asymmetrical properties, ... 
Explicit numerical algorithms for stochastic differential equations and their applications in data science and optimization
(The University of Edinburgh, 20201130)In this thesis, we focus on the analysis of a new generation of explicit numerical algorithms for (nonlinear) random systems and their applications in computational statistics, nonconvex optimization, data science, and ... 
Bayesian Semiparametic estimation of densities with unknown support
(The University of Edinburgh, 20201130)We address the nonregular semiparametric problem of estimating a boundary point of the support of an unknown density, under local asymptotic exponentiality. The aim is to find the limiting marginal posterior distribution ... 
Dispersive hydrodynamics in a nonlocal nonlinear medium
(The University of Edinburgh, 20210731)Dispersive shock wave (DSW), sometimes referred to as an undular bore in fluid mechanics, is a nonlinear dispersive wave phenomenon which arises in nonlinear dispersive media for which viscosity effects are negligible ... 
Parahoric Hitchin fibration
(The University of Edinburgh, 20210731)We study parahoric Hitchin fibrations over complex smooth projective curves. These are analogues of the Grothendieck resolutions in the classical Springer theory. In particular, we describe the generic fibers of the ... 
Bayesian inference for ocean transport and diffusivity fields from Lagrangian trajectory data
(The University of Edinburgh, 20201130)Eddy diffusion is commonly used to characterise subgridscale mixing of tracer quantities in geophysical fluid simulations. Limited by data availability, estimating eddy diffusivity from observational data remains challenging. ... 
Multiperiod sales districting problem
(The University of Edinburgh, 20210731)In the sales districting problem, we are given a set of customers and a set of salesmen in some area. The salesmen have to provide services at the customers' locations to satisfy their requirements. The task is to allocate ... 
Facility location problems and games
(The University of Edinburgh, 20210731)We concern ourselves with facility location problems and games wherein we must decide upon the optimal locating of facilities. A facility is considered to be any physical location to which customers travel to obtain a ... 
The Stability of Hyperbolic PDEs in String Theory, Particle Physics and Cosmology
(The University of Edinburgh, 20200901)In this thesis we study hyperbolic PDEs arising from general relativity and the standard model of particle physics. In particular we prove the asymptotic stability of special solutions of these PDEs against small initial ... 
Stochastic analysis and partial differential equations: theory and numerics
(The University of Edinburgh, 20201130)This thesis is concerned with problems at the interface of stochastic analysis and partial differential equations (PDEs). In particular, we focus on two different classes of problem: the transport of measures under the ... 
Granular media at multiple scales: mathematical analysis, modelling and computation
(The University of Edinburgh, 20200728)There are many challenges in modelling granular media, in particular due to hard particle interactions such as collisions. Modelling and simulating at a microscopic level produces very accurate results, but simulations ... 
Inertiagravitywaves in geostrophic turbulence
(The University of Edinburgh, 20200728)The dynamics of the atmosphere and ocean can be decomposed into a slow, largescale component, in near geostrophic and hydrostatic balance, and a fast component consisting mostly of inertia–gravity waves (IGWs). These waves ... 
Parameter clustering in Bayesian functional PCA of neuroscientific data
(The University of Edinburgh, 20200722)This thesis provides novel methodologies for functional Principal Component Analysis of dependent time series (curves) with particular emphasis on those arising from neuroscientific experiments. In this context, the ... 
Random geometric graphs and data structures: discrete estimations of the continuous
(The University of Edinburgh, 20200706)In recent years, there have been significant efforts to develop rigourous geometric and topological methodologies to better understand data sets, with the view of performing machine learning tasks such as spectral ... 
Evidence evaluation and functional data analysis
(The University of Edinburgh, 20200625)In forensic contexts, evidence gathered are valuable in suggesting possible crimes. The problems forensic scientists are often interested in are whether evidence found at the scene of the crime match those that are found ... 
McKeanVlasov equations: a probabilistic and pathwise approach
(The University of Edinburgh, 20200625)This thesis divides neatly into four collections of results. In the first (Part II), we provide existence and uniqueness results along with several properties for a class of McKeanVlasov Equations having random ... 
Analysis and applications of dynamic density functional theory
(The University of Edinburgh, 20200625)Classical ﬂuid mechanics and, in particular, the general compressible NavierStokesFourier equations, have long been of great use in the prediction and understanding of the ﬂow of ﬂuids in various scenarios. While the ... 
Multiplicative latent force models
(The University of Edinburgh, 20200625)Latent force models (LFM) are a class of ﬂexible models of dynamic systems, combining a simple mechanistic model with the ﬂexibility of an additive inhomogeneous Gaussian process (GP) forcing term. These hybrid models ...