Speaker
Description
Dvoretzky’s theorem is one of the classical results of high-dimensional geometry: every sufficiently high-dimensional normed space contains almost Euclidean subspaces of logarithmic dimension. Geometrically, this means that compact convex symmetric sets have high dimensional sections that are close to being elliptical.
In this talk, we discuss two extensions of this result. In the first one, we give complex and quaternionic versions of the theorem. The second direction is geometric. We interpret the original Dvoretzky's Theorem in terms of the radial function of the convex set. Then, using the Hopf fibration, we show that, under a suitable convexity condition, Dvoretzky’s theorem gives almost Euclidean behavior for functions on appropriate projective subspaces.