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SUMMARY:High-dimensional tennis balls -  Kasia Wyczesany\, University of C
 ambridge 
DTSTART:20191120T160000Z
DTEND:20191120T170000Z
UID:TALK135199@talks.cam.ac.uk
CONTACT:84031
DESCRIPTION:In this talk I will explain what a high-dimensional tennis bal
 l is\, how one can construct it and give a motivation why such an object m
 ight be of interest by connecting it to V. Milman's question: Let $C>1$ an
 d $\\e>0$ be constants and let $k$ be an integer. Is it true that for suff
 iciently large $N$\, every normed space $X$ that is $C$-equivalent to $\\e
 ll_2^N$ has a $k$-dimensional subspace that is $(1+\\e)$-complemented and 
 $(1+\\e)$-equivalent to $\\ell_2^k$? This is joint work with W.T. Gowers.
LOCATION:MR14\, Centre for Mathematical Sciences
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