In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. ...

Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are ...

In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or ...

A study Of Quine's Set Theory

In Berger's classification of Riemannian holonomy groups there are several infinite families and two exceptional cases: the groups Spin(7) and G_2. This thesis is mainly concerned with 7-dimensional manifolds with ...

Let Y be a quartic hypersurface in P^4 with terminal singularities. The Grothendieck-Lefschetz theorem states that any Cartier divisor on Y is the restriction of a Cartier divisor on P^4 . However, no such result holds ...

Geophysical research has long been interdisciplinary, with many phenomena on the Earth's surface involving multiple, linked processes that are best understood using a combination of techniques. This is particularly true ...

GaugThe first half of the thesis concerns Abelian vortices and Yang-Mills theory. It is proved that the 5 types of vortices recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations ...

Quantum mechanics, which describes the behaviour of matter and energy on very small scales, is one of the most successful theories in the history of science. Einstein's theory of special relativity, which describes the ...