Our research groups cover a broad range of Mathematics, Statistics and Operational Research. Please visit the School of Mathematics home pages for more information.

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  • Evidence evaluation and functional data analysis 

    Chang, Ya-Ting (The University of Edinburgh, 2020-06-25)
    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 ...
  • McKean-Vlasov equations: a probabilistic and pathwise approach 

    Salkeld, William John (The University of Edinburgh, 2020-06-25)
    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 McKean-Vlasov Equations having random ...
  • Analysis and applications of dynamic density functional theory 

    Mills-Williams, Rory (The University of Edinburgh, 2020-06-25)
    Classical fluid mechanics and, in particular, the general compressible Navier-Stokes-Fourier 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 

    Tait, Daniel J. (The University of Edinburgh, 2020-06-25)
    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 ...
  • Accelerated sampling schemes for high dimensional systems 

    Martinsson, Anton (The University of Edinburgh, 2020-04-06)
    In this thesis we discuss accelerated sampling schemes for high dimensional systems, for example molecular dynamics (MD). The development of these methods is fundamental to the effective study of a large class of problems, ...
  • Some questions related to the Analyst’s TST and a conjecture of Carleson 

    Villa, Michele (The University of Edinburgh, 2020-03-17)
    This thesis is constituted by two independent parts. In the first part we discuss several problems which relate to the Analyst's Travelling Salesman Theorem of Peter Jones and the theories of uniformly rectifiable sets and ...
  • Quantalic spectra of semirings 

    Manuell, Graham Richard (The University of Edinburgh, 2020-06-25)
    Spectrum constructions appear throughout mathematics as a way of constructing topological spaces from algebraic data. Given a localic semiring R (the pointfree analogue of a topological semiring), we define a spectrum of ...
  • Derived contraction algebra 

    Booth, Matt Paul (The University of Edinburgh, 2019-11-25)
    All minimal models of a given variety are linked by special birational maps called flops, which are a type of codimension two surgery. A version of the Bondal–Orlov conjecture, proved by Bridgeland, states that if X and ...
  • Monte-Carlo based numerical methods for a class of non-local deterministic PDEs and several random PDE systems 

    Tan, Shuren (The University of Edinburgh, 2019-11-28)
    In this thesis, we will investigate McKean-Vlasov SDEs (McKV-SDEs) on Rd,: ; where coefficient functions b and σ satisfy sufficient regularity conditions and fWtgt2[0;T ] is a Wiener process. These SDEs correspond to a ...
  • Landscape of Hamiltonian phase spaces: on the foundations and generalizations of one of the most powerful ideas of modern science 

    Zapata-Carratala, Carlos (The University of Edinburgh, 2019-11-28)
    In this thesis we aim to revise the fundamental concept of phase space in modern physics and to devise a way to explicitly incorporate physical dimension into geometric mechanics. To this end we begin with a nearly sel ...
  • Randomized iterative methods for linear systems: momentum, inexactness and gossip 

    Loizou, Nicolas (The University of Edinburgh, 2019-11-28)
    In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem ...
  • Moduli space of supersymmetric black holes in five dimensions 

    Breunhölder, Veronika (The University of Edinburgh, 2019-11-28)
    This thesis presents a classification of all asymptotically at, supersymmetric and biaxisymmetric (i.e. possessing a U(1)2-symmetry) soliton and black hole solutions to five-dimensional minimal supergravity. In particular, ...
  • Mutation frequencies in a birth-death branching process 

    Cheek, David Michael (The University of Edinburgh, 2019-08-20)
    A growing population of cells accumulates genetic mutations. We study stochastic models of this process. Cells divide and die as a branching process, and a cell's genetic information is a sequence of nucleotides which ...
  • Cancer recurrence times and early detection from branching process models 

    Avanzini, Stefano (The University of Edinburgh, 2019-11-28)
    Cancer is among the leading causes of death worldwide. While primary tumors are often treated effectively, they can spawn secondary cancers called metastases which dramatically decrease chances of survival. In order to ...
  • Stochastic dispersive PDEs with additive space-time white noise 

    Tolomeo, Leonardo (The University of Edinburgh, 2019-11-28)
    In this thesis, we will discuss the Cauchy problem for some nonlinear dispersive PDEs with additive space-time white noise forcing. We will focus on two different models: the stochastic nonlinear beam equation (SNLB) ...
  • Quantitative propagation of chaos of McKean-Vlasov equations via the master equation 

    Tse, Alvin Tsz Ho (The University of Edinburgh, 2019-11-28)
    McKean-Vlasov stochastic differential equations (MVSDEs) are ubiquitous in kinetic theory and in controlled games with a large number of players. They have been intensively studied since McKean, as they pave a way to ...
  • Stochastic PDEs beyond standard monotonicity: well posedness and regularity of solutions 

    Neelima (The University of Edinburgh, 2019-11-28)
    Nonlinear stochastic partial differential equations (SPDEs) are used to model wide variety of phenomena in physics, engineering, finance and economics. In many such models the equations exhibit super-linear growth. In ...
  • Tilting theory of contraction algebras 

    August, Jennifer Louise (The University of Edinburgh, 2019-07-01)
    This thesis focuses on a class of finite dimensional symmetric algebras arising in geometry, known as contraction algebras. The main results presented here combine to give a complete description of the derived equivalence ...
  • Applications of the blow-up technique in singularly perturbed chemical kinetics 

    Miao, Zhouqian (The University of Edinburgh, 2019-07-01)
    This thesis addresses the geometric analysis of traveling front propagation in singularly perturbed dynamical systems. The study of front propagation in reaction-diffusion systems has received a significant amount of ...
  • Basis preconditioning in interior point methods 

    Schork, Lukas Marius (The University of Edinburgh, 2019-07-01)
    Solving normal equations AAᵀx = b, where A is an m x n matrix, is a common task in numerical optimization. For the efficient use of iterative methods, this thesis studies the class of preconditioners of the form BBᵀ , where ...

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