Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

Geometrical Finiteness, Holography, and the BTZ Black Hole

We show how a theorem of Sullivan provides a precise mathematical statement of a 3d holographic principle, that is, the hyperbolic structure of a certain class of 3d manifolds is completely determined in terms of the corresponding Teichmuller space of the boundary. We explore the consequences of this theorem in the context of the Euclidean BTZ black hole in three dimensions.Comment: 6 pages, Latex, Version to appear in Physical Review Letter

Dirichlet fundamental domains and complex-projective varieties

We prove that for every finitely-presented group G there exists a 2-dimensional irreducible complex-projective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas.Comment: 1 figur

Newsprint coverage of smoking in cars carrying children : a case study of public and scientific opinion driving the policy debate

Acknowledgements Date of Acceptance:17/10/2014 Acknowledgements: This project was funded by Cancer Research UK (MC_U130085862) and the Scottish School of Public Health Research. Cancer Research UK and the Scottish School of Public Health Research was not involved in the collection, analysis, and interpretation of data, writing of the manuscript or the decision to submit the manuscript for publication. Shona Hilton, Karen Wood, Josh Bain and Chris Patterson are funded by the UK Medical Research Council as part of the Understandings and Uses of Public Health Research programme (MC_UU_12017/6) at the MRC/CSO Social and Public Health Sciences Unit, University of Glasgow. We thank Alan Pollock who provided assistance with coding.Peer reviewedPublisher PD

Systematic mechanical assessment of consolidants for canvas reinforcement under controlled environment

In conservation, adhesives are commonly used for the consolidation of canvases, yet their impact upon the canvas longevity has raised some concerns amongst conservators. As such, this study presents a testing protocol developed to assess the performance of commonly-used adhesives (natural animal glue and synthetic Beva® 371) and a newly developed nanocellulose consolidant, nanofibrillated nanocellulose (CNF). This includes their effect on the visual appearance, consolidation, and response of the mechanical properties of the treated canvases to programmed changes in relative humidity (RH). Scanning electron microscopy (SEM) images of animal glue- and Beva® 371-treated canvases revealed the presence of adhesive and consolidant on and in-between cotton fibres. The consolidants form bridges linking and connecting the cotton fibres and holding them together, whereas the CNF treatment, formed a visible continuous and dense surface coating. None of the treatments induced any discernible colour change. Controlled environment mechanical testing was performed in two ways: by applying a linearly increasing static force at fixed RH (Young’s modulus) and by applying a dynamic force together with a programmed RH cycling between 20 and 80% (RH dependent viscoelastic properties). CNF gave a higher value of Young’s modulus than either of the two commonly-used materials. Measurements at different values of RH (20 and 80%) demonstrated for all the treated canvases that at the lower value (RH 20%) Young’s modulus values were higher than at the higher value (RH 80%). Besides, the dynamic mode showed that the rate of response in all cases was rapid and reversible and that the nanofibrillated cellulose treated sample showed the highest variation in storage (or elastic) modulus measured at the end of RH plateaux (20 and 80% RH). Thus CNF appears to be a promising material given its higher mechanical performance. The protocol developed in this study has enabled us to examine and compare candidate materials for the consolidation of canvases systematically, using testing parameters that remained relevant to the field of canvas conservation

The longitude problem from the 1700s to today: An international and general education physics course

For instructors wishing to use physics as part of an international or general education course, the framework for a course based on the “longitude problem” from the 1700s is described. The longitude problem is teeming with basic principles of physics and astronomy, which makes it ideal for a non-science-major-based college-level course. This paper summarizes the longitude problem in the context of conceptual physics and astronomy and outlines an appropriate curriculum. Specifics on teaching such a course in London, as part of an international studies program, are discussed

Anosov representations: Domains of discontinuity and applications

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)