Imagination and visualization of geometric and topological forms in space:about some formal, aesthetic and perceptual aspects of mathematics

Our world, at different scales, abounds in knotted and linked rings. Qualitative similarities may be observed between forms of the microscopic world, as well as between those of the macroscopic world; and by extracting the structures, it is possible to study their dynamics thanks to topological concepts and methods. The seminar is aimed at showing, first, that knots and links are scale-independent objects carrying an amount of precious information and signification on the emergence of new forms and structures in the mathematical and real world, and secondly, that a rich manifold of interesting surfaces and spaces can be constructed from knots and braids by applying diagrammatic and projection techniques. This will allow us to illustrate some striking relationships and common features between topological, natural and aesthetic objects and spaces. With the help of some relevant examples from knots and knotted spaces, we will propose a method for thinking by diagrams and transformation in order to grasp some processes underlying the generation of objects and events.