Edited Volumes

Knots, Low-Dimensional Topology and Applications

Knots, Low-Dimensional Topology and Applications. Edited by Colin C. Adams, Cameron McA. Gordon, Vaughan F.R. Jones, Louis H. Kauffman, Sofia Lambropoulou, Kenneth C. Millett, Jozef H. Przytycki, Renzo L. Ricca, Radmila Sazdanovic (Springer-Nature, Switzerland, 2019), ISBN 978-3-030-16030-2.

From the Preface:

This collection of papers originates from the conference: International Conference on Knots, Low-Dimensional Topology and Applications—Knots in Hellas 2016. The conference was held at the International Olympic Academy, Ancient Olympia, Greece from July 17–23, 2016. The conference was an occasion to celebrate the 70th birthday of Louis H. Kauffman.

The goal of this international cross-disciplinary conference was to enable exchange of methods and ideas as well as exploration of fundamental research problems in the fields of knot theory and low-dimensional topology, from theory to applications in sciences like biology and physics, and to provide high-quality interactions across fields and generations of researchers, from graduate students to the most senior researchers. In this sense, this volume is one of the few published books covering and combining these topics.


Helicity, Structures and Singularity in Fluid and Plasma Dynamics

Helicity, Structures and Singularity in Fluid and Plasma Dynamics (IUTAM Symposium, Venice, Italy, April 11-15, 2016). Edited by Yasuhide Fukumoto, Renzo L. Ricca, Philip Boyland and Jens Eggers (IOP Science 2018).

The Proceedings of the Symposium have been published as a special issue of Fluid Dynamics Research, Volume 50, Issue 1, 2018, IOP Science.

Lectures on Topological Fluid Mechanics

Lectures on Topological Fluid Mechanics. Edited by Renzo L. Ricca (Springer-Verlag, Heidelberg, Germany, 2009), ISBN 978-3-642-00836-8.

Since its online publication there have been a total of 15.360 eBook downloads on SpringerLink (August, 2020).

From the Preface:

It seems very appropriate to publish these Lectures in the 150th anniversary of the publication of Helmholtz’s seminal paper on vortex motion (1858), that may be regarded as the pioneering work on fundamental questions in topological fluid mechanics. The field is going through a period of great revival, benefiting from the formidable progress in knot theory and differential topology, on the one hand, and mathematical and computational fluid dynamics, on the other. It is therefore with great pleasure that I warmly thank the contributors to this volume for providing such an interesting collection of valuable research papers. All the material presented here is actually an update of the original material presented in the lecture notes delivered by six of us, on the occasion of a CIME Summer School (of the Unione Matematica Italiana) in 2001, a School that I had the honour and pleasure to organize and direct in Cetraro, a charming location on the rugged coastline of southern Italy.


An Introduction to the Geometry and Topology of Fluid Flows

An Introduction to the Geometry and Topology of Fluid Flows. Edited by Renzo L. Ricca (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001), ISBN 1-4020-0207-6.

From the Preface:

Leading experts present a modern introduction to the study of the geometry and topology of fluid flows. From basic notions on curves and surfaces, topology and recent developments in knot theory, the reader is gradually led to explore the fascinating world of geometric and topological structures in fluid mechanics. Fundamental aspects of dynamical systems in general fluid flows, vortex dynamics, magnetohydrodynamics, fluid reconnections and singularities are discussed in a pedagogical manner, with many examples and more than 150 illustrations.

A universal zoo of geodesics, chaotic orbits, braided flows and separatrices roll and wrap around magnetic knots and vortex links, where continual flows and singularities become `alive and kicking’. The opening article by H.K. Moffatt sets the pace by proposing eight outstanding problems.