Mathematics, School of: Recent submissions
Now showing items 120 of 487

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 ... 
On Lpsolvability of stochastic integrodifferential equations
(The University of Edinburgh, 20210731)In this thesis, we investigate the Lpsolvability of a class of (possibly) degenerate stochastic integrodifferential equations (SIDEs) of parabolic type, which includes the Zakai equation in nonlinear filtering for jump ... 
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 ...