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MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participati...
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International ...
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many oth...
This book constitutes the proceedings of the 5th Conference on Computability in Europe, CiE 2009, held in Heidelberg, Germany, during July 19-24, 2009. The 34 papers presented together with 17 invited lectures were carefully reviewed and selected from 100 submissions. The aims of the conference is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. It is the largest international meeting focused on computability theoretic issues.
Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and strin...
A Stitch in Line: Mathematics and One-Stitch Sashiko provides readers with instructions for creating hitomezashi items with minimum outlay. The reader is guided through the practical steps involved in creating each design, and then the mathematics which underpins it is explained in a friendly, accessible way. This is a fantastic book for anyone who is interested in recreational mathematics and/or fibre arts and can be a useful resource for teaching and learning mathematical concepts in a fun and engaging format. Features Numerous full-colour photographs of hitomezashi stitch patterns which have been mathematically designed. Suitable for readers of all mathematical levels and backgrounds — no prior knowledge is automatically assumed. A compressed encoding for recording and designing hitomezashi patterns to be stitched or drawn. Accessible explanations and explorations of mathematical concepts inherent in, or illustrated by, hitomezashi patterns.
This book presents 57 peer-reviewed papers from the 12th Conference on Traffic and Granular Flow (TGF) held in Washington, DC, in July 2017. It offers a unique synthesis of the latest scientific findings made by researchers from different countries, institutions and disciplines. The research fields covered range from physics, computer science and engineering and they may be all grouped under the topic of "Traffic and Granular Flow". The main theme of the Conference was: "From Molecular Interactions to Internet of Things and Smart Cities: The Role of Technology in the Understanding and the Evolution of Particle Dynamics".
A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.
This book focuses on the design and testing of large-scale, distributed signal processing systems, with a special emphasis on systems architecture, tooling and best practices. Architecture modeling, model checking, model-based evaluation and model-based design optimization occupy central roles. Target systems with resource constraints on processing, communication or energy supply require non-trivial methodologies to model their non-functional requirements, such as timeliness, robustness, lifetime and “evolution” capacity. Besides the theoretical foundations of the methodology, an engineering process and toolchain are described. Real-world cases illustrate the theory and practice tested by the authors in the course of the European project ARTEMIS DEMANES. The book can be used as a “cookbook” for designers and practitioners working with complex embedded systems like sensor networks for the structural integrity monitoring of steel bridges, and distributed micro-climate control systems for greenhouses and smart homes.
This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a well-posed road from simple lattice models to CFTs. Structured in two parts, the book begins by exploring several two-dimensional lattice models, their phase transitions, and their conjectural connection with CFT. Through these lattice models and their local fields, the fundamental ideas and results of two-dimensional CFTs emerge, with a special emphasis on the Unitary Minimal Models of CFT. Delving into the delicate ideas that lead to the classification of these CFTs, the authors discuss the assumpti...