Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Title
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An introduction to applications of wavelet benchmarking with seasonal adjustment
(WileyJournal of the Royal Statistical Society: Series A (Statistics in Society), 20161105)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 ...

An upper bound for the pseudoisotopy stable range
(SpringerMathematische Annalen, 20170801)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, ...

Arithmetic invariant theory and 2descent for plane quartic curves
(Mathematical Sciences PublishersAlgebra & Number Theory, 20160927)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 ...

Arithmetic structure in sets of integers
(University of Cambridge, 20080520)This dissertation deals with four problems concerning arithmetic structures in dense sets of integers. In Chapter 1 we give an exposition of the stateoftheart technique due to Pintz, Steiger and Szemer edi which yields ...

Asymptotics of Partial Density Functions for Divisors
(SpringerThe Journal of Geometric Analysis, 20160919)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 ...

Automorphisms of free products of groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20130205)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 ...

Automorphy of some residually dihedral Galois representations
(Springer, 20150508)We establish the automorphy of some families of 2dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the socalled ‘Taylor–Wiles hypothesis’. We apply this to the problem ...

Automorphy of some residually S$_5$ Galois representations
(SpringerMathematische Zeitschrift, 2016)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 ...

Autonomous Pseudomonoids
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20090425)In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. ...

Balanced metrics on twisted Higgs bundles
(SpringerMathematische Annalen, 2016)

Balanced semisimple filtrations for tilting modules
(American Mathematical SocietyRepresentation Theory, 20170308)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 ...

Bayesian Nonparametric Ordination for the Analysis of Microbial Communities
(Taylor & FrancisJournal of the American Statistical Association, 20170710)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 ...

Bayesian regularization of the length of memory in reversible sequences
(WileyJournal of the Royal Statistical Society: Series B (Statistical Methodology), 20151016)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 historydependent lengths of memory which characterize these models and to predict ...

Bounded Height in Families of Dynamical Systems
(Oxford University PressInternational Mathematics Research Notices, 20170829)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 ...

Bounding cohomology for low rank algebraic groups
(University of CambridgeDPMMSHomerton, 20170801)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 ...

Brownian motion correlation in the peanosphere for κ >8
(ElsevierAnnales de l'institut Henri Poincare (B) Probability and Statistics, 20171101)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 ...

Bulk eigenvalue statistics for random regular graphs
(Institute of Mathematical StatisticsAnnals of Probability, 2016)We consider the uniform random dregular 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 ...

Categories of spaces built from local models
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity Hall, 20160628)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 wellknown ...

Chaos and Entropic Chaos in Kac's Model Without High Moments
(Institute of Mathematical StatisticsElectronic Journal of Probability, 20130827)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 ...

Characterisation of gradient flows on finite state Markov chains
(Institute of Mathematical StatisticsElectronic Communications in Probability, 20150329)In his 2011 work, Maas has shown that the law of any timereversible continuoustime Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. ...