This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2–6, 2018, at Université du Québec à Montréal, Montréal, Québec, Canada. Boyer's contributions to research in low-dimensional geometry and topology, and to the Canadian mathematical community, were recognized during the conference. The articles cover a broad range of topics related, but not limited, to the topology and geometry of 3-manifolds, properties of their fundamental groups and associated representation varieties.

This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.

Calculations and Simulations of Low-Dimensional Materials A comprehensive guide to methods for calculating and simulating the properties of low-dimensional materials Two-dimensional materials are those, such as graphene and 2D oxides, whose thickness is so small as to approach the atomic scale. Potential applications for these materials exist in an enormous range of scientific and industrial fields. A previous era of low-dimensional materials focused on direct experimentation to demonstrate the properties, reactions, and potential applications of these materials; however, in recent years, calculation and simulation have been shown to have considerable predictive power, reducing the period between design and deployment of these potentially critical materials. Calculations and Simulations of Low-Dimensional Materials offers the first comprehensive survey of this exciting new approach to low-dimensional materials. It guides readers through the foundational physics and through a range of calculation and simulation methods, each with different predictive capacities. Mastery of these methods will enable readers to narrowly tailor the properties of particular materials towards real-world applications, providing confidence in the underlying mechanics and in the range of possible outcomes. Calculations and Simulations of Low-Dimensional Materials readers will also find: Broad coverage of material properties, including electronic, spin, magnetic, photonic, optical, electrochemical and transport properties Discussion of potential applications in areas such as electronics, spintronics, and valleytronics Examination of further potential applications regarding quantum Hall phase, photonics, optoelectronics, multiferroic, and photocatalysis Calculations and Simulations of Low-Dimensional Materials is a useful reference for materials scientists, electrochemists, inorganic chemists, physical chemists, photochemists, and the libraries that support these professions.