16.30 Friday 15 June 2018
The Cost of the Sphere Eversion and the 16-pi Conjecture
How much does it cost…to knot a closed simple curve ? To cover the sphere twice ? to realize such or such homotopy class ? …etc.
All these questions consisting of assigning a “canonical” number and possibly an optimal “shape” to a given topological operation are known to be mathematically very rich and to bring together notions and techniques from topology, geometry and analysis. In this talk we will concentrate on the operation consisting of everting the 2 sphere in the 3 dimensional space. Since Smale’s proof in 1959 of the existence of such an operation the search for effective realizations of such eversions has triggered a lot of fascination and work in the mathematical community. The absence in nature of matter that can interpenetrate and the quasi impossibility, up to the advent of virtual imaging, to experience this deformation is maybe the reason for the difficulty to develop an intuitive approach on the problem.
We will present the optimization due to Sophie Germain of conformally invariant elastic energy for the eversion. Our efforts will finally bring us to consider more closely an integer number together with a mysterious minimal surface.
Please note the change of room! The talk will take place in the Salle des Profs at 16:30. Coffee, tea and biscuits will be served in the foyer by the Salle des Profs, from 16:00. The Salle des Profs is on the 9th floor of building NO, of the Campus de la Plaine. Maps of the campus and directions are available here.
15 June 2018