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  • Scaling limit of critical systems in random geometry 

    Powell, Ellen Grace (2017-11-25)
    This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider Schramm--Loewner evolutions, the Gaussian free field, ...
  • Well-posedness and scattering of the Chern-Simons-Schrödinger system 

    Lim, Zhuo Min (2017-10-01)
    The subject of the present thesis is the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in two spatial dimensions with a long-range electromagnetic field. The present thesis studies two ...
  • Deformation theory of Cayley submanifolds 

    Moore, Kimberley (2017-05-04)
    Cayley submanifolds are naturally arising volume minimising submanifolds of $Spin(7)$- manifolds. In the special case that the ambient manifold is a four-dimensional Calabi--Yau manifold, a Cayley submanifold might be a ...
  • Isospectral algorithms, Toeplitz matrices and orthogonal polynomials 

    Webb, Marcus David (2017-04-01)
    An isospectral algorithm is one which manipulates a matrix without changing its spectrum. In this thesis we study three interrelated examples of isospectral algorithms, all pertaining to Toeplitz matrices in some fashion, ...

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