Preface

Abstract

This online volume contains a selection of papers arising from two workshops organised withinthe six-month programme Topological Dynamics in the Physical and Biological Sciences held atthe Isaac Newton Institute for Mathematical Sciences, Cambridge, from July to December 2012.The first of these was a ‘satellite workshop’ held at the International Centre for MathematicalSciences (ICMS), Edinburgh, 15-19 October 2012, under the title Tangled Magnetic Fields inAstro- and Plasma Physics, and with Scientific Organising Committee: Konrad Bajer (Warsaw),Mitchell Berger (Exeter), Steve Cowley (Culham Centre for Fusion Energy), Andrew Gilbert(Exeter), Gunnar Hornig (Dundee), and Clare Parnell (St Andrews). The second was theworkshop Quantised Flux in Tightly Knotted and Linked Systems held at the Newton Institute, 3-7 December 2012, with Scientific Organising Committee: Natalia Berloff (DAMTP, Cambridge),Anne-Christine Davis (DAMTP, Cambridge), Jason Cantarella (University of Georgia), ThomasKephart (Vanderbilt University), Paul Sutcliffe (Durham University), and Tanmay Vachaspati(Arizona State University). Videos of the lectures given at this second workshop can be viewed at http://www.newton.ac.uk/webseminars.The papers published here follow a natural progression through the following topics: helicityand related invariants of magnetic fields in ideal MHD; relaxation under topological constraints;lower bounds on magnetic energy; current and vortex filaments; applications in the solarcorona, tokamak plasmas, and cyclone dynamics; higher-order invariants; topology of curves andsurfaces, and energy measures; tight knots; applications to Bose-Einstein condensates, QCD, andcosmic superstring theory. Some of the papers span more than one of these areas.We owe a great debt of gratitude to Konrad Bajer, who was one of the guiding spirits behindthe whole Newton Institute program, and who took particular responsibility for the SatelliteWorkshop at ICMS, Edinburgh. Konrad fell seriously ill in June 2014, having completed muchof the editorial work for these Proceedings. Following an operation at the end of July, heremained optimistic of a complete recovery, but sadly this was not to be, and he died from aparticularly malignant form of cancer on 29th August. The funeral was held in Warsaw on 5thSeptember. Konrad's warmth of personality and generosity of spirit will be remembered by allwho participated in these workshops and in the wider Newton Institute program.The Isaac Newton Institute provided an ideal environment for informal interactions before andafter both these workshops. We wish to express our thanks to the Director and staff of theInstitute for their tireless efforts to ensure the success of the whole program; also to the staff ofICMS, Edinburgh, for their expert hosting of the satellite workshop.