Seminar on Banach and Metric Space Geometry

Date: March 24, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Petros Valettas, University of Missouri

Title: Variance estimates and Dvoretzky's theorem

Abstract: Abstract. The concentration of measure implies that for any norm on ℝn there exist many subspaces on which the restriction of the norm has very small distortion and whose dimension depends on the oscillations of the norm in the unit sphere of the ambient space. In this talk we will explain how the fluctuations of the norm can quantify the tightness of this phenomenon. For this end we will present a variance-sensitive small deviation inequality for convex functions of gaussian vectors. Time permitting we will show applications of the latter to the asymptotic theory of normed spaces. (Joint work with G. Paouris).