Mathematics, School of: Recent submissions
Now showing items 1-20 of 536
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Certain geometric maximal functions in harmonic analysis
(The University of Edinburgh, 2023-07-17)The broad theme of the thesis is of geometric maximal functions associated to curved surfaces. We produce novel results about two maximal functions of different types, presented in two parts of the thesis. In the first ... -
Examining the effects of magnetic fields in neutron star mergers through numerical simulations
(The University of Edinburgh, 2023-07-11)In this thesis, we present simulations of merging binary neutron stars, carried out using the publicly available FLASH code framework. These are 3D Newtonian magnetohydrodynamic simulations, in which we have included ... -
On slope stability of tangent sheaves on smooth toric Fano varieties
(The University of Edinburgh, 2023-06-30)We prove that number 82 in the Batyrev-Sato classi cation of smooth toric Fano 4-folds is an explicit counterexample of Picard rank 4 to a long-standing conjecture due to Peternell - the fi rst known counterexample of ... -
Geometric singular perturbation theory for reaction-diffusion systems
(The University of Edinburgh, 2023-06-16)Geometric singular perturbation theory (GSPT) has proven to be an invaluable tool for the study of multiple time scale ordinary differential equations (ODEs). The extension of the theory to partial differential equations ... -
Solution methods for some variants of the vehicle routing problem
(The University of Edinburgh, 2023-05-19)The Vehicle Routing Problem (VRP) is among the most important and widely researched problems in the field of combinatorial optimization. It fits a large variety of applications across many industries faced with the ... -
Estimates of space derivatives for functions of non-autonomous and McKean-Vlasov processes. Application to uniform weak error bounds induced by the approximating subsampled particle system
(The University of Edinburgh, 2023-05-16)This thesis is split in three parts, all of which obtain derivative estimates for the solution to the backward Kolmogorov equation associated to diverse stochastic process and study their application to uniform weak error ... -
Numerical framework for solving PDE-constrained optimization problems from multiscale particle dynamics
(The University of Edinburgh, 2023-04-21)In this thesis, we develop accurate and efficient numerical methods for solving partial differential equation (PDE) constrained optimization problems arising from multiscale particle dynamics, with the aim of producing a ... -
Regularised variational schemes for non-gradient systems, and large deviations for a class of reflected McKean-Vlasov SDE
(The University of Edinburgh, 2023-03-27)This thesis consists of two parts. The first part constructs entropy regularised variational schemes for a range of evolutionary partial differential equations (PDEs), not necessarily in gradient flow form, with a focus ... -
Non-Lorentzian geometry of fluids and strings
(The University of Edinburgh, 2023-03-16)Non-Lorentzian geometry is a branch of geometry where, roughly speaking, the notion of a metric is replaced by something else. We begin by providing an overview of non-Lorentzian geometries, and we describe how they as ... -
Moment polyptychs and the equivariant quantisation of hypertoric varieties
(The University of Edinburgh, 2023-03-01)In this thesis, we develop a method to investigate the geometric quantisation of a hypertoric variety from an equivariant viewpoint, in analogy with the equivariant Verlinde formula for Higgs bundles. We do this by first ... -
Fukaya category and (open) Gromov-Witten invariants
(The University of Edinburgh, 2023-02-22)This thesis contributes to the problem of obtaining both open and closed Gromov-Witten invariants from the Fukaya category. For closed invariants, the main ingredient is the cyclic open-closed map which maps the cyclic ... -
Foldy-wouthuysen transformation and its generalisations
(University of Edinburgh, 1961)The purpose of this thesis is to survey the developments in the field opened up in 1950 by Foldy and Wouthuysen. The investigations to be discussed here have all been concerned with the derivation of certain transformations ... -
Gauge invariance in quantum electrodynamics
(University of Edinburgh, 1961)The object of this dissertation is to present a survey of papers written on gauge invariance in the past decade. Up till 1955 mainly c-number gauges were used. The generalisation to q-number gauges, however, has introduced ... -
Problems related to uniform rectifiability and bi-Lipschitz images
(The University of Edinburgh, 2023-02-15)In the first part of this thesis we give a new sufficient condition for a set to be uniformly d-rectifiable. The condition is that through each point of the set, there are d-many uniformly spread out line segments contained ... -
Computational modelling and optimal control of interacting particle systems: connecting dynamic density functional theory and PDE-constrained optimization
(The University of Edinburgh, 2023-02-07)Processes that can be described by systems of interacting particles are ubiquitous in nature, society, and industry, ranging from animal flocking, the spread of diseases, and formation of opinions to nano-filtration, ... -
Deep-water and shallow-water limits of the intermediate long wave equation: from deterministic and statistical viewpoints
(The University of Edinburgh, 2023-02-06)In this thesis, we study the convergence problem for the intermediate long wave equation (ILW) from deterministic and statistical viewpoints. ILW models the internal wave propagation of the interface in a two-layer fluid ... -
Power system adequacy: on two-area models and the capacity procurement decision process
(The University of Edinburgh, 2023-01-20)In this work, we explore methodological extensions to modelling practices in power system adequacy for single-area and two-area systems. Specifically, we build on top of some of the practices currently in use in Great ... -
Conditional densities of partially observed jump diffusions
(The University of Edinburgh, 2023-01-19)In this thesis, we study the fi ltering problem for a partially observed jump diffusion (Zₜ)ₜɛ[ₒ,T] = (Xₜ, Yₜ)tɛ[ₒ,T] driven by Wiener processes and Poisson martingale measures, such that the signal and observation noises ... -
Donaldson-Thomas theory and cohomological Hall algebras of character stacks
(The University of Edinburgh, 2023-01-18)Given a smooth finitely generated algebra with a potential one can study the refined Donaldson-Thomas theory of its moduli stack of representations via motivic or cohomological methods. In this thesis we focus on fundamental ... -
Presolve, crash and software engineering for HiGHS
(The University of Edinburgh, 2023-01-18)The efficient computational solution of linear optimization problems is generally enhanced significantly by using a "presolve" procedure to process the problem logically in order to reduce the dimension of the problem to ...
