edited by Luciano Boi (École des Hautes Études en Sciences Sociales, Centre de Mathématiques, and LUTH, Observatoire de Paris-Meudon, France)

The collection of papers forming this volume is intended to provide a deeper study of some mathematical and physical subjects which are at the core of recent developments in the natural and living sciences. The book explores some far-reaching interfaces where mathematics, theoretical physics, and natural sciences seem to interact profoundly. The main goal is to show that an accomplished movement of geometrisation has enabled the discovery of a great variety of amazing structures and behaviors in physical reality and in living matter. The diverse group of expert mathematicians, physicists and natural scientists present numerous new results and original ideas, methods and techniques. Both academic and interdisciplinary, the book investigates a number of important connections between mathematics, theoretical physics and natural sciences including biology.

• Mathematical Ideas and Techniques in Classical and Quantum Physics:T-Duality, Functional Equation, and Noncommutative String Spacetime (M Lapidus)
  • On the Soliton-Particle Dualities (F Hélein & J Kouneiher)
• Knots in Mathematics and in Nature:
  • Knots (L H Kauffman)
  • Topological Knots Models in Physics and Biology (L Boi)
• Mathematical and Logical Modeling in the Natural Sciences and Living Systems:
  • Beyond Modeling: A Challenge for Applied Mathematics (P T Saunders)
  • Fondements Cognitifs de la Géométrie et Expérience de L'espace (A Berthoz)
  • The Reasonable Effectiveness of Mathematics and Its Cognitive Roots (G Longo)
  • Pathways of Deductions (A Carbone)
  • Phénoménologie et Théorie des Catégories (F Patras)