This book provides a remarkable collection of contributions written by some of the most accredited world experts in the modern area of Knotted Fields. Scope of the book is to provide an updated view of some of the key aspects of contemporary research, with the purpose to cover basic concepts and techniques commonly used in the context of Knotted Fields. The material is presented to help the interested reader to become familiar with the fundamentals, from fluid flows to electromagnetism, from knot theory to numerical visualization, while presenting the new ideas and results in an accessible way to beginners and young researchers. No advanced knowledge is required, and at the end of each chapter, key references are provided to offer further information on particular topics of interest. All those keen on modern applications of topological techniques to the study of knotted fields in mathematical physics will find here a valuable and unique source of information. The work will be of interest to many researchers in the field.

It provides a comprehensive review of the rapidly expanding field of Knotted Fields It highlights role and effects of low dimensional topology on the dynamics and energetics of physical knotted fields It covers a vast array of topics that illustrate the wide use of Knotted Fields in pure and applied science

Autorentext

Renzo L. Ricca After graduating from Politecnico di Torino, Ricca went to Trinity College, Cambridge, where he studied Mathematics. In 1991, he was awarded a J.T. Knight Prize in Mathematics while preparing his doctorate. He received his PhD from Cambridge University with a dissertation entitled Geometric and Topological Aspects of Vortex Filament Motion, under the supervision of Professor H.K. Moffatt. In 1992, he was elected research fellow, then senior research fellow and lecturer at University College London. In 2000, he lectured in Japan as a JSPS Fellow, and in 2004, he moved back to Italy as professor of Mathematical Physics at the University of Milano-Bicocca. From 2016, he is a distinguished guest professor of Beijing University of Technology, and from 2023, he is an affiliate member of the SKCM2 World Premier Institute of Hiroshima University. During his academic life, he visited many, prestigious research centers, such as the Institute for Advanced Study (Princeton), the Kavli Institute for Theoretical Physics (Santa Barbara), the Newton Institute (Cambridge), and organized and directed several advanced schools and conferences, including some long-term intensive research programs such as Geometry and Topology of Fluid Flows at the Newton Institute (2000), and Knots and Applications at the De Giorgi Mathematics Research Centre of the Scuola Normale di Pisa (2011). He edited 4 books and has published more than 80 papers on applications of geometric and topological aspects in vortex dynamics, magnetohydrodynamics and quantum fluids in condensates.

Xin Liu is a professor of Theoretical Physics at Beijing University of Technology (BJUT). He obtained his PhD in Mathematics in 2007 from the University of Queensland, and then he moved to the University of Sydney (USYD) working as a USYD postdoctoral research fellow, and teaching faculty. After a short visiting fellowship to the Isaac Newton Institute of Mathematical Sciences in Cambridge, he joined BJUT as an associate professor in 2014 with a Beijing Overseas Talent Aggregation Project-Youth Fellowship. His research area is theoretical physics and applied mathematics, with particular interest in topological aspects of knotted fields in classical and quantum fluids, new topological materials (Chern insulators and semi-metals), knot theory, 3- and 4-manifold invariants in topological quantum field theory. His academic services include refereeing for the Israel and Chinese National Science Foundations, for Mathematical Reviews, and many other international peer-reviewed journals.

Inhalt

• A Topological Approach to Vortex Knots and Links.- From Knot Invariants to Knot Dynamics.- Multi-Valued Potentials in Topological Field Theory.- Excitable and Magnetic Knots.- Spiral Waves in Excitable Media: Seifert Framing and Helicity.- Designing Knotted Fields in Light and Electromagnetism.- Tangled Vortex Lines: Dynamics, Geometry and Topology of Quantum Turbulence.- An Introduction to Knotplot.- Using the Homflypt Polynomial to Compute Knot Types.