Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...

We give examples of closed orientable graph 3-manifolds having a fundamental group which is not a subgroup of GL(4, F) for any field F. This answers a question in the Kirby problem list from 1977 which is credited to the ...

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using ...

A symplectic manifold gives rise to a triangulated A∞-category, the derived Fukaya category, which encodes information on Lagrangian submanifolds and dynamics as probed by Floer cohomology. This survey aims to give some ...

In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest ...

In the post-war years, the theory of 3-dimensional manifolds has developed tremendously. On the one hand, Bing and Moise have proved that 3-manifolds can be triangulated, and that the Hauptvermutung (that any two triangulations ...

This work constructs and compares different kinds of categorified cohomology of a locally contractible topological space X. Fix a commutative ring k of characteristic 0 and also denote by k the differential graded category ...

This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a large individual participant data (IPD) meta-analysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...

Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...

The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ...

NOTE : The mathematical symbols in the abstract do not always display correctly in this text field. Please see the abstract in the thesis for the definitive abstract. ABSTRACT: This dissertation is in two parts, each ...

We analyse the steady-state behaviour of two different models with collaborating queues: that is, models in which "customers" can be served by many types of "servers", and "servers" can process many types of "customers". The ...

I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear ...

A symplectic manifold is a smooth manifold M together with a choice of a closed non-degenerate two-form. Recent years have seen the importance of associating an A∞-category to M, called its Fukaya category, in helping ...

Mendelian randomization is an epidemiological method for using genetic variation to estimate the causal effect of the change in a modifiable phenotype on an outcome from observational data. A genetic variant satisfying ...

This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements ...

My thesis focuses on the parameterisation and estimation of graphical models, based on the concept of hyper and meta Markov properties. These state that the parameters should exhibit conditional independencies, similar to ...

Abstract Background Genome-wide association studies (GWAS) are a widely used study design for detecting genetic causes of complex diseases. Current studies provide good coverage of common causal SNPs, but not rare ones. A ...

Density estimation is a fundamental statistical problem. Many methods are either sensitive to model misspecification (parametric models) or difficult to calibrate, especially for multivariate data (nonparametric smoothing ...