### Recent Submissions

• #### Scaling limit of critical systems in random geometry ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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, ...