# Mathematical Sciences Research Institute

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# Seminar

GFA Main Seminar: "Irrational" Convexity: geometric means and the power functions for convex bodies. September 14, 2017 (11:00 AM PDT - 12:00 PM PDT)
Parent Program: Geometric Functional Analysis and Applications MSRI: Simons Auditorium
Speaker(s) Vitali Milman (Tel-Aviv University)
Description No Description
Video
Abstract/Media

Do we have enough examples of Convex Bodies?

Is diversity of our standard examples enough to understand Convexity?

In the talk we demonstrate many different constructions which are analogous to constructions of irrational numbers from rationals. In particular we show how the geometric mean (and lambda-geometric means) may be defined for any centrally symmetric convex compact bodies K  and  T. We also construct  K^a for any centrally symmetric K and -1 < a < 1, and also Log K  for K containing  the euclidean ball D (and K = -K). Note,  the power |a| cannot be above 1 in the definition of power !

Based on joint results with Liran Rotem.