On the Heegaard Floer homology of Dehn surgery and unknotting number

n this thesis we generalise three theorems from the literature on Heegaard Floer homology and Dehn surgery: one by Ozsv ́ath and Szab ́o on deficiency symmetries in half-integral L -space surgeries, and two by Greene which use Donaldson’s diagonali- sation theorem as an obstruction to integral and half-integral L -space surgeries. Our generalisation is two-fold: first, we eliminate the L -space conditions, opening these techniques up for use with much more general 3-manifolds, and second, we unify the integral and half-integral surgery results into a broader theorem applicable to non- zero rational surgeries in S 3 which bound sharp, simply connected, negative-definite smooth 4-manifolds. Such 3-manifolds are quite common and include, for example, a huge number of Seifert fibred spaces. Over the course of the first three chapters, we begin by introducing background material on knots in 3-manifolds, the intersection form of a simply connected 4- manifold, Spin- and Spin c -structures on 3- and 4-manifolds, and Heegaard Floer ho- mology (including knot Floer homology). While none of the results in these chapters are original, all of them are necessary to make sense of what follows. In Chapter 4, we introduce and prove our main theorems, using arguments that are predominantly algebraic or combinatorial in nature. We then apply these new theorems to the study of unknotting number in Chapter 5, making considerable headway into the extremely difficult problem of classifying the 3-strand pretzel knots with unknotting number one. Finally, in Chapter 6, we present further applications of the main theorems, ranging from a plan of attack on the famous Seifert fibred space realisation problem to more biologically motivated problems concerning rational tangle replacement. An appendix on the implications of our theorems for DNA topology is provided at the end.Open Acces

John Hansen

Profile of John Hansen (High Court judge in New Zealand) interviewed at the time of his visit to IALS as part of a project to research attitudes and approaches to case management in Britain. He explains some of the approaches his country has taken to judicial reform. Published in the Profile section of Amicus Curiae - Journal of the Institute of Advanced Legal Studies and its Society for Advanced Legal Studies. The Journal is produced by the Society for Advanced Legal Studies at the Institute of Advanced Legal Studies, University of London

Adsorption and grafting on colloidal interfaces studied by scattering techniques

The adsorption of polymer and surfactant molecules onto colloidal particles or droplets in solution can be characterized non-destructively by scattering techniques. In a first part, the general framework of Dynamic Light Scattering, Small Angle Neutron and X-ray Scattering for the determination of the structure of adsorbed layers, and namely of the density profile, is presented. We then review recent studies of layers of the model polymer poly(ethylene oxide), as homopolymer or part of a block copolymer. In this field, scattering with contrast variation has been shown to be a powerful tool to obtain a detailed description of the layer structure. Adsorption of chemically more complex systems, including polyelectrolytes, polymer complexes, grafted chains and biomacromolecules are also discussed in this review, as well as surfactant adsorption

Phenomenology of Majorons

Majorons are the Goldstone bosons associated to lepton number and thus closely connected to Majorana neutrino masses. Couplings to charged fermions arise at one-loop level, including lepton-flavor-violating ones that lead to decays $\ell\to \ell' J$, whereas a coupling to photons is generated at two loops. The typically small couplings make massive majorons a prime candidate for long-lived dark matter. Its signature decay into two mono-energetic neutrinos is potentially detectable for majoron masses above MeV.Comment: 4 pages. Contributed to the 13th Patras Workshop on Axions, WIMPs and WISPs, Thessaloniki, May 15 to 19, 201

Public technology: challenging the commodification of knowledge

Discusses the role of technology in commodifying teaching, that is making it a marketable commodity, and describes a number of examples of how academic staff around the world are using open technologies to make teaching and learning both accessible to a wider public, and to involve the wider public in student learning

Ideation and Appropriation: Wittgenstein on Intellectual Property

This paper provides a critique of the contemporary notion of intellectual property based on the consequences of Wittgenstein's “private language argument”. The reticence commonly felt toward recent applications of patent law, e.g., sports moves, is held to expose erroneous metaphysical assumptions inherent in the spirit of current IP legislation. It is argued that the modern conception of intellectual property as a kind of natural right, stems from the mistaken internalist or Augustinian picture of language that Wittgenstein attempted to diffuse. This view becomes persuasive once it is shown that a complete understanding of the argument against private language must include Wittgenstein's investigation of the role of the will in the creative process. It is argued that original thought is not born by decree of the will, but engendered by a public context of meaning and value. What marks a person as a genius is, therefore, according to Wittgenstein, not some sovereign capacity of conceptual world-making, but merely a propitious dose of intellectual courage

Regression with Distance Matrices

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the response can be developed using standard methods. We call scoring the transformation from a new observation to a score while backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.Comment: 18 pages, 7 figure