Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Title
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3manifolds everywhere
A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3manifold with totally geodesic boundary. These subgroups can be taken to be quasiisometrically embedded. This ...

A 2adic automorphy lifting theorem for unitary groups over CM fields
(SpringerMathematische Zeitschrift, 2016)We prove a ‘minimal’ type automorphy lifting theorem for 2adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2.

A 3manifold group which is not four dimensional linear
(ElsevierJournal of Pure and Applied Algebra, 20140128)We give examples of closed orientable graph 3manifolds 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 ...

A Counter Example to Cercignani’s Conjecture for the d Dimensional Kac Model
(SpringerJournal of Statistical Physics, 20120821)Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ...

A finite dimensional approach to Donaldson's Jflow
Consider a projective manifold with two distinct polarisations $L_1$ and $L_2$. From this data, Donaldson has defined a natural flow on the space of Kähler metrics in $c_1$($L_1$), called the Jflow. The existence of a ...

A Fully Automatic Theorem Prover with HumanStyle Output
(SpringerJournal of Automated Reasoning, 20160611)This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians.

A Functional Approach to Deconvolve Dynamic Neuroimaging Data
(Taylor & FrancisJournal of the American Statistical Association, 20151120)Positron Emission Tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are ...

A Liouville hyperbolic souvlaki
(Institute of Mathematical StatisticsElectronic Journal of Probability, 20170425)We construct a transient boundeddegree graph no transient subgraph of which embeds in any surface of finite genus. Moreover, we construct a transient, Liouville, boundeddegree, Gromov–hyperbolic graph with trivial ...

A Markov Model of a Limit Order Book: Thresholds, Recurrence, and Trading Strategies
We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the ...

A More General Pandora Rule?
(ElsevierJournal of Economic Theory, 20151102)In a model introduced by Weitzman an agent called Pandora opens boxes sequentially, in whatever order she likes, discovers prizes within, and optimally stops. Her aim is to maximize the expected value of the greatest ...

A Paleylike graph in characteristic two
(Journal of Combinatorics, 2016)The Paley graph is a wellknown selfcomplementary pseudorandom graph, defined over a finite field of odd order. We describe an attempt at an analogous construction using fields of even order. Some properties of the graph ...

A short proof that every finite graph has a treedecomposition displaying its tangles
(ElsevierEuropean Journal of Combinatorics, 20160608)We give a short proof that every finite graph (or matroid) has a treedecomposition that displays all maximal tangles. This theorem for graphs is a central result of the graph minors project of Robertson and Seymour and ...

A Symplectic Prolegomenon
(American Mathematical SocietyBulletin of the American Mathematical Society, 2014)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 ...

Abelian quotients of mapping class groups of highly connected manifolds
(SpringerMathematische Annalen, 20151012)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 ...

Acylindrical Hyperbolicity, nonsimplicity and SQuniversality of groups splitting over $\mathbb{Z}$
(De GruyterJournal of Group Theory, 20160915)We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\mathbb{Z}$ cannot be simple. We also obtain SQuniversality in most cases, for instance a balanced group (one where if two powers ...

Algebraic boundaries of Hilbert's SOS cones
(Cambridge University PressCompositio Mathematica, 20121015)We study the geometry underlying the difference between nonnegative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be ...

Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
(Université Paul SabatierAnnales de la Faculté des Sciences de Toulouse, 2016)We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anticanonical case implying the ...

Alpha Invariants and KStability for General Polarizations of Fano Varieties
(Oxford University PressINTERNATIONAL MATHEMATICS RESEARCH NOTICES, 20140926)We provide a sufficient condition for polarisations of Fano varieties to be Kstable in terms of Tian’s alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system ...

Ample subvarieties and qample divisors
(ElsevierAdvances in Mathematics, 20120320)We introduce a notion of ampleness for subschemes of any codimension using the theory of qample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ...

An explicit upper bound for the Helfgott delta in SL(2,p)
(ElsevierJournal of Algebra, 20140923)Helfgott proved that there exists a δ > 0 such that if S is a symmetric generating subset of SL(2, p)containing 1 then either S^3=SL(2, p)or S^3 ≥S^1+ δ. It is known that δ ≥ 1/3024. Here we show that δ ≤ (log_2 (7) ...