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 varieties: positivity, K-stability and more 

    Viswanathan, Nivedita (The University of Edinburgh, 2022-04-11)
    This thesis is about Fano varieties and their properties. We will determine the K-stability of certain singular del Pezzo surfaces and smooth Fano 3-folds, the existence of cylinders in singular del Pezzo surfaces, and ...
  • Iterative methods for solving stochastic optimal control problems 

    Kerimkulov, Bekzhan (The University of Edinburgh, 2022-04-04)
    Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Therefore, most of the time, they have to be solved numerically. In this ...
  • Regularized interior point methods for convex programming 

    Pougkakiotis, Spyros (The University of Edinburgh, 2022-03-23)
    Interior point methods (IPMs) constitute one of the most important classes of optimization methods, due to their unparalleled robustness, as well as their generality. It is well known that a very large class of convex ...
  • Bayesian methods for biomarker evaluation and disease diagnosis 

    Garrido Guillén, Javier (The University of Edinburgh, 2022-03-22)
    Accurate diagnosis of disease is of fundamental importance in medical research and clinical practice. For such reason, the role that diagnostic testing and screening play is undeniable. The major goal of a diagnostic ...
  • Methods for the analysis of oscillatory integrals and Bochner-Riesz operators 

    Wheeler, Reuben (The University of Edinburgh, 2022-03-21)
    For a smooth surface Γ of arbitrary codimension, one can consider the Lp mapping properties of the Bochner-Riesz multiplier m(ζ) = dist(ζ,Γ)^α φ(ζ), where α > 0 and φ is an appropriate smooth cutoff function. Even for ...
  • Constructing and classifying five-dimensional black holes using integrability 

    Tomlinson, Fred (The University of Edinburgh, 2022-03-17)
    In this thesis we look at the problem of nding and classifying stationary and biaxisymmetric solutions in ve-dimensional theories of gravity, using particular hidden symmetries. We consider three theories: the electrostatic ...
  • Statistical modelling of environmental extremes 

    Auld, Graeme (The University of Edinburgh, 2022-03-16)
    This thesis is concerned with the development of theory and statistical methodologies that may be used to analyse environmental extremes. As extreme environmental events are often associated with large economic costs and ...
  • Mixed-mode oscillations in singularly perturbed three-timescale systems 

    Kaklamanos, Panagiotis (The University of Edinburgh, 2022-02-22)
    In this work, we are concerned with the dynamics of three-dimensional, three-timescale systems of ordinary differential equations. Systems with two timescales have been extensively studied, while the theory of systems ...
  • Randomly assembled cyclic multi-block ADMM: a fast method for large-scale linearly constrained quadratic optimization 

    Mihic, Kresimir (The University of Edinburgh, 2022-02-22)
    This work is motivated by a simple question: how to find a relatively good solution to a very large optimization problem in a limited amount of time. We consider the linearly constrained convex minimization model with ...
  • Bayesian inverse problems 

    Rodrigues, Jenovah (The University of Edinburgh, 2021-11-27)
    We consider linear, mildly ill-posed inverse problems in separable Hilbert spaces under Gaussian noise, whose covariance operator is not identity (i.e. it is not a white noise problem), and use the Bayesian approach to ...
  • Thermal effects on nonlinear optical beam propagation in nematic liquid crystals 

    Khan, Cassandra Chaya (The University of Edinburgh, 2021-11-27)
    This thesis examines in detail the study of nonlinear wave phenomena arising in different contexts in applied nonlinear optics. In particular, it explores the intricate nonlinear interplay between light and matter using ...
  • Low regularity well-posedness of the modified and the generalized Korteweg-de Vries equations 

    Chapouto, Andreia (The University of Edinburgh, 2021-11-27)
    In this thesis, we study the well-posedness of the modified and generalized Korteweg-de Vries equations on the one-dimensional torus. We first consider the complex-valued modified Korteweg-de Vries equation (mKdV). We ...
  • Extreme precision and extreme complexity: source modelling and data analysis development for the laser interferometer space antenna 

    Burke, Alexander Iain; Burke, Ollie (The University of Edinburgh, 2021-11-27)
    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 d-dimensional analyst's Travelling Salesman theorem for arbitrary sets in Euclidean space 

    Hyde, Matthew (The University of Edinburgh, 2021-11-27)
    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 

    Grassie, Ross (The University of Edinburgh, 2021-11-27)
    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 

    McIntyre, Finlay; Dupree McIntyre, Finlay (The University of Edinburgh, 2021-11-27)
    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 p-median problems with radius constraints; and, Its application to clustering with feature selection 

    Martín del Campo Barraza, Minerva Montserrat (The University of Edinburgh, 2021-07-31)
    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 Lp-solvability of stochastic integro-differential equations 

    Wu, Sizhou (The University of Edinburgh, 2021-07-31)
    In this thesis, we investigate the Lp-solvability of a class of (possibly) degenerate stochastic integro-differential 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 

    Mkrtchyan, Anna (The University of Edinburgh, 2021-07-31)
    In this thesis we study algebras that appear in di erent generalisations of the well-known Schur-Weyl duality. This classical result gives a remarkable connection between the irreducible finite-dimensional representations ...
  • On the McKean-Vlasov dynamics with or without common noise 

    Hammersley, William Richard Philip (The University of Edinburgh, 2021-07-31)
    McKean-Vlasov stochastic differential equations may arise from a probabilistic interpretation of certain non-linear PDEs or as the limiting behaviour of mean field particle systems (those whose interactions are through ...

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