Mathematics, School of
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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Fano threefolds and algebraic families of surfaces of Kodaira dimension zero
(The University of Edinburgh, 2010-11-24)The thesis consists of four chapters. First chapter is introductory. In Chapter 2, we recall some basic facts from the singularity theory of algebraic varieties (see Section 2.2) and the theory of minimal models (see ... -
Inertia-gravity wave generation: a WKB approach
(The University of Edinburgh, 2011-06-28)The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance ... -
Moduli of bundles on local surfaces and threefolds
(The University of Edinburgh, 2010-11-24)In this thesis we study the moduli of holomorphic vector bundles over a non-compact complex space X, which will mainly be of dimension 2 or 3 and which contains a distinguished rational curve ℓ ⊂ X. We will consider the ... -
Parabolic boundary value problems with rough coefficients
(The University of Edinburgh, 2018-11-29)This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has ... -
Crepant resolution conjecture for Donaldson-Thomas invariants via wall-crossing
(The University of Edinburgh, 2018-11-29)Let Y be a smooth complex projective Calabi{Yau threefold. Donaldson-Thomas invariants [Tho00] are integer invariants that virtually enumerate curves on Y. They are organised in a generating series DT(Y) that is interesting ... -
Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation
(The University of Edinburgh, 2018-11-29)This thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial ... -
Many server queueing models with heterogeneous servers and parameter uncertainty with customer contact centre applications
(The University of Edinburgh, 2018-11-29)In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates ... -
A correspondence between null and ordinary geodesics, its properties and Straneo's unified theory
(The University of Edinburgh, 1933) -
Contributions to the theory of hypergeometric functions and other papers
(The University of Edinburgh, 1940) -
Singularities of noncommutative surfaces
(The University of Edinburgh, 2018-11-29)The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also be singular, in the sense that they have infinite ... -
On k-normality and regularity of normal projective toric varieties
(The University of Edinburgh, 2018-07-02)We study the relationship between geometric properties of toric varieties and combinatorial properties of the corresponding lattice polytopes. In particular, we give a bound for a very ample lattice polytope to be k-normal. ... -
Bridgeland stability conditions, stability of the restricted bundle, Brill-Noether theory and Mukai's program
(The University of Edinburgh, 2018-11-29)In [Bri07], Bridgeland introduced the notion of stability conditions on the bounded derived category D(X) of coherent sheaves on an algebraic variety X. This topic is originally inspired by concepts in string theory and ... -
Stochastic, distributed and federated optimization for machine learning
(The University of Edinburgh, 2017-11-30)We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that ... -
Design of reliable aerospace system architecture
(The University of Edinburgh, 2018-11-29)Reliability and redundancy of safety-critical network systems is a paramount issue in system engineering. Be it in evaluating existing network systems or solving optimization problems for designing network systems, it ... -
Statistical methods for the testing and estimation of linear dependence structures on paired high-dimensional data: application to genomic data
(The University of Edinburgh, 2018-07-02)This thesis provides novel methodology for statistical analysis of paired high-dimensional genomic data, with the aimto identify gene interactions specific to each group of samples as well as the gene connections that ... -
Heuristic methods for solving two discrete optimization problems
(The University of Edinburgh, 2018-07-02)In this thesis we study two discrete optimization problems: Traffic Light Synchronization and Location with Customers Orderings. A widely used approach to solve the synchronization of traffic lights on transport networks ... -
Two geometric inequalities in harmonic analysis
(The University of Edinburgh, 2010)We study two geometric inequalities in harmonic analysis. -
Theorems in the tensor calculus, with applications to relativity
(The University of Edinburgh, 1932) -
The use of proof plans in tactic synthesis
(The University of Edinburgh, 1993)We undertake a programme of tactic synthesis. We first formalize the notion of a tactic as a rewrite rule, then give a correctness criterion for this by means of a reflection mechanism in the constructive type theory ... -
Data sampling strategies in stochastic algorithms for empirical risk minimization
(The University of Edinburgh, 2018-07-02)Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data ...
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