Before adjustment, low and high frequency data sets from national accounts are frequently inconsistent. Benchmarking is the procedure used by economic agencies to make such data sets consistent. It typically involves ...

We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than (2n - 2). In order to do so, we define new characteristic classes for block bundles, extending our earlier work with Ebert, ...

Given a smooth plane quartic curve C over a field $\textit{k}$ of characteristic 0, with Jacobian variety $\textit{J}$, and a marked rational point P $\in$ C($\textit{k}$), we construct a reductive group $\textit{G}$ and ...

This dissertation deals with four problems concerning arithmetic structures in dense sets of integers. In Chapter 1 we give an exposition of the state-of-the-art technique due to Pintz, Steiger and Szemer edi which yields ...

We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$ . Assuming the data in question is ...

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 ...

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 ...

Let $\textit{F}$ be a totally real field and $\textit{p}$ an odd prime. We prove an automorphy lifting theorem for geometric representations $\rho$ : $\textit{G}_F$ → GL$_2$($\bar{\Bbb Q}_p$) which lift irreducible residual ...

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

Let $ U_l$ be a quantum group at an $ l$th root of unity, obtained via Lusztig's divided powers construction. Many indecomposable tilting modules for $ U_l$ have been shown to have what we call a balanced semisimple ...

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency ...

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 ...

Let a, b ∈ $\bar{\mathbb{Q}}$ be such that exactly one of a and b is an algebraic integer, and let f$_{t}$(z) := z$^{2}$ + t be a family of polynomials parameterized by t ∈ $\bar{\mathbb{Q}}$. We prove that the set of all ...

Let G be a semisimple linear algebraic group over an algebraically closed field of prime characteristic. In this thesis we outline the theory of such groups and their cohomology. We then concentrate on algebraic groups in ...

The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$-Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent ...

We consider the uniform random d-regular graph on N vertices, with d ∈ [N$^{\alpha}$,N$^{2/3−\alpha}$] for arbitrary α > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the ...

Many of the classes of objects studied in geometry are defined by first choosing a class of nice spaces and then allowing oneself to glue these local models together to construct more general spaces. The most well-known ...

In this paper we present a new local Lévy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying ...

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. ...