Departmental Colloquia

Autumn 2017

The colloquia (unless otherwise stated) will take place on Tuesdays at 3.00pm in Room D103 (25 Godron Street). See the map for further details. There will be a small reception afterwards in Mathematics Room 502 (25 Gordon Street). If you require any more information on the  Departmental Colloquia please contact Prof Dima Vassiliev e-mail: d.vassiliev AT ucl.ac.uk or tel: 020-7679-2442.

14 November 2017

Speaker: Dr Tristan Rivière (Institute for Mathematical Research, ETH Zurich)

Title: The Cost of the Sphere Eversion and the 16\pi Conjecture
Abstract:

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 works in the math 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 of Sophie Germain 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.