Mathematics, School of
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Derived contraction algebra
(The University of Edinburgh, 20191125)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 ... 
MonteCarlo based numerical methods for a class of nonlocal deterministic PDEs and several random PDE systems
(The University of Edinburgh, 20191128)In this thesis, we will investigate McKeanVlasov SDEs (McKVSDEs) 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
(The University of Edinburgh, 20191128)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
(The University of Edinburgh, 20191128)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
(The University of Edinburgh, 20191128)This thesis presents a classification of all asymptotically at, supersymmetric and biaxisymmetric (i.e. possessing a U(1)2symmetry) soliton and black hole solutions to fivedimensional minimal supergravity. In particular, ... 
Mutation frequencies in a birthdeath branching process
(The University of Edinburgh, 20190820)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
(The University of Edinburgh, 20191128)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 spacetime white noise
(The University of Edinburgh, 20191128)In this thesis, we will discuss the Cauchy problem for some nonlinear dispersive PDEs with additive spacetime white noise forcing. We will focus on two different models: the stochastic nonlinear beam equation (SNLB) ... 
Quantitative propagation of chaos of McKeanVlasov equations via the master equation
(The University of Edinburgh, 20191128)McKeanVlasov 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
(The University of Edinburgh, 20191128)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 superlinear growth. In ... 
Tilting theory of contraction algebras
(The University of Edinburgh, 20190701)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 blowup technique in singularly perturbed chemical kinetics
(The University of Edinburgh, 20190701)This thesis addresses the geometric analysis of traveling front propagation in singularly perturbed dynamical systems. The study of front propagation in reactiondiffusion systems has received a significant amount of ... 
Basis preconditioning in interior point methods
(The University of Edinburgh, 20190701)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 ... 
Properties and advances of probabilistic and statistical algorithms with applications in finance
(The University of Edinburgh, 20190701)This thesis is concerned with the construction and enhancement of algorithms involving probability and statistics. The main motivation for these are problems that appear in finance and more generally in applied science. ... 
Automated theory formation in pure mathematics
(The University of Edinburgh, 2001)The automation of specific mathematical tasks such as theorem proving and algebraic manipulation have been much researched. However, there have only been a few isolated attempts to automate the whole theory formation ... 
Matrix representation of symmetric groups
(The University of Edinburgh, 1947)The Thesis consists of two parts. In part I, a concentrated summary of the symmetric group, its matrix representations and characters, is given. In part II, the irreducible matrix representations of the symmetric groups ... 
The development of statistical theory in Britain, 18651925: a historical and sociological perspective
(The University of Edinburgh, 1978)This thesis discusses the development of statistical theory in Britain in the period 1865 to 1925, and attempts to account for this development as an institutional and an intellectual phenomenon. Close connections are ... 
Analytical properties of certain probability distributions
(The University of Edinburgh, 1938)This research has been carried out on Dr Aitken's suggestion. The first chapter is largely a recapitulation of known results which I have learnt from Dr Aitken, here arranged for convenience of reference later in the thesis. 
Allied subsets of topological groups and linear spaces
(The University of Edinburgh, 1967)1, Basic theory, 4  2. Allied sets in linear spaces, 17  3. Cauchy nets and completeness, 29  4, Subgroups and subspaces. 39  5. Locally compact subsets of topological linear spaces. 46  6. ... 
On problems in the estimation of statistical parameters from samples grouped in broad categories
(The University of Edinburgh, 1952)When a number of individuals are observed in respect of some characteristic whose occurrence may be expressed in terms of a numerical variable, it often happens that what is recorded for each individ ual is not the ...