Mathematics

We show that the space of convex bodies in the n-dimensional Euclidean space, which are not reduced to points or segments, up to translations and homotheties, is parametrized by a convex subset of an infinite dimensional hyperbolic space. The ambient Lorentzian structure is given by a linear extension of the intrinsic area form. We also study the particular case n=3, which gives us information on the space of non-negative Alexandrov metrics on the 2-sphere.
The understanding of the talk does not require any specific knowledge: the mathematics presented here are not very difficult - nor rely on any deep theory - but the point of view presented seems to be new.
This is a joint work with François Fillastre (Cergy-Pontoise University/Paris).