We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...

In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay ...

In his 2011 work, Maas has shown that the law of any time-reversible continuoustime Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. ...

We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called ‘Taylor–Wiles hypothesis’. We apply this to the problem ...

We study regularity properties of solutions to the Dirichlet problem for the complex Homogeneous Monge-Ampere equation. We show that for certain boundary data on P^1 the solution Φ to this Dirichlet problem is connected ...

We show that the motive of the Hilbert scheme of length-n subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, ...

We study F-saturation games, first introduced by Füredi, Reimer and Seress [4] in 1991, and named as such by West [5]. The main question is to determine the length of the game whilst avoiding various classes of graph, ...

This thesis studies the structure of categories of polynomials, the diagrams that represent polynomial functors. Specifically, we construct new models of intensional dependent type theory based on these categories. Firstly, ...

Mandarin Chinese is characterized by being a tonal language; the pitch (or F0) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in ...

In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both ...

A motive over a field k is of abelian type if it belongs to the thick and rigid subcategory of Chow motives spanned by the motives of abelian varieties over k. This paper contains three sections of independent interest. ...

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of ...

We explore transversals of finite index subgroups of finitely generated groups. We show that when H is a subgroup of a rank n group G and H has index at least n in G then we can construct a left transversal for H which ...

The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on ...

We compute the abelianisations of the mapping class groups of the manifolds W²ⁿ_g = g(Sⁿ × Sⁿ) for n ≥ 3 and g ≥ 5. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group ...

We introduce a norm on the space of test configurations, called the minimum norm. We conjecture that uniform K-stability is equivalent to the existence of a constant scalar curvature Kähler metric. This uniformity is ...

Variable order Markov chains have been used to model discrete sequential data in a variety of fields. A host of methods exist to estimate the history-dependent lengths of memory which characterize these models and to predict ...

We give results on when a finitely generated torsion free group does or does not embed in SL(2, C). For instance if we glue two copies of the figure 8 knot along its torus boundary then the fundamental group of the resulting ...

We study a fundamental problem in social choice theory, the selection of a member of a set of agents based on impartial nominations by agents from that set. Studied previously by Alon et al. [Proceedings of TARK, 2011, pp. ...