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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Recent Submissions

  • Bayesian analysis of jointly heavy-tailed data 

    Palacios Ramırez, Karla Vianey (The University of Edinburgh, 2022-11-29)
    This thesis develops novel Bayesian methodologies for statistical modelling of heavy-tailed data. Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of main-stream random probability ...
  • Size and shape of things: magnitude, diversity, homology 

    Roff, Emily (The University of Edinburgh, 2022-11-29)
    This thesis has to do with magnitude: a numerical invariant of enriched categories which, when specialized to examples such as posets, groupoids or metric spaces, turns out to encompass a variety of size-related quantities ...
  • Pre-trained solution methods for unit commitment 

    Sugishita, Nagisa (The University of Edinburgh, 2022-11-16)
    This thesis aims to improve the solution methods for the unit commitment problem, a short-term planning problem in the energy industry. In particular, we focus on Dantzig-Wolfe decomposition with a column generation ...
  • On the dynamics of measure flows and multi-agent and mean-field financial games 

    Platonov, Vadim (The University of Edinburgh, 2022-11-24)
    This thesis comprises two different collection of results. We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depends on measure flows. We distinguish the ...
  • Optimal coordination of multiple price-maker electricity storage units for price arbitrage 

    Solà Vilalta, Albert (The University of Edinburgh, 2022-10-11)
    Decarbonization of the electricity supply via the integration of renewable generation poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take ...
  • Stability, Hilbert scheme and PT moduli of genus four curves and failure of the MMP/Wall-crossing correspondence 

    Rezaee, Fatemeh (The University of Edinburgh, 2022-11-24)
    Inspired by concepts in string theory, the notion of stability conditions on triangulated categories was introduced by Bridgeland in 2002. Its impact across mathematics includes the solutions of classical problems in ...
  • Change detection in spatiotemporal SAR data for deforestation monitoring 

    Hansen, Johannes (The University of Edinburgh, 2022-08-22)
    Forests play a vital role in the wellbeing of our planet. Large and small scale deforestation across the globe is threatening the stability of our climate, forest biodiversity, and therefore the preservation of fragile ...
  • Preconditioned iterative methods for optimal control problems with time-dependent PDEs as constraints 

    Leveque, Santolo (The University of Edinburgh, 2022-06-27)
    In this work, we study fast and robust solvers for optimal control problems with Partial Differential Equations (PDEs) as constraints. Speci cally, we devise preconditioned iterative methods for time-dependent PDE-constrained ...
  • Bayesian analysis of nonstationary extremes 

    Lee, Junho (The University of Edinburgh, 2022-06-27)
    Extreme value theory (EVT) provides theoretical foundation to assess the probability of rare and extreme events. This thesis provides novel Bayesian semiparametric models for capturing the behaviour of extreme events and ...
  • Role of structure in oscillatory integral estimates 

    Green, John (The University of Edinburgh, 2022-06-22)
    Although oscillatory integrals intrinsically depend only on measure-theoretic properties of the phase and amplitude functions, in practice most techniques for deriving estimates invoke structural information either implicitly ...
  • Stochastic dynamics and partitioned algorithms for model parameterization in deep learning 

    Vlaar, Tiffany Joyce (The University of Edinburgh, 2022-06-16)
    In this thesis, we study model parameterization for deep learning applications. Part of the mathematical foundation for this work lies in stochastic differential equations and their constrained counterparts. We will study ...
  • Local and global analysis of geometric partial differential equations and their application to curvature flow problems 

    Espin, Tim (The University of Edinburgh, 2022-06-15)
    “An analytical approach to many problems in geometry leads to the study of partial differential equations.” (A. V. Pogorelov, Foreword to The Minkowski Multidimensional Problem) This thesis concerns itself with three ...
  • Uncertainty quantification in seismic interferometry 

    Ayala-Garcia, Daniella (The University of Edinburgh, 2022-06-13)
    It is a well-established principle that cross-correlating wavefield observations at different receiver locations yields new responses that, under certain conditions, provide a useful estimate of the Green's function between ...
  • Multijoints and multilinear duality 

    Michael Chi Yung, Tang (The University of Edinburgh, 2022-05-25)
    The joints problem is related to geometric questions at the heart of harmonic analysis. In three dimensions, a joint is a point of intersection of three lines that do not lie within a common plane. Given a collection of ...
  • Quantum symmetric pairs in topological field theory 

    Weelinck, Tim Anne Nils (The University of Edinburgh, 2019-11-28)
    [No Deposit Agreement]
  • Factorisation homology and skein categories of surfaces 

    Cooke, Juliet (The University of Edinburgh, 2019-11-28)
    [No Deposit Agreement]
  • 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 ...

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