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CATEGORIES:Combinatorics Seminar
SUMMARY:Inequalities on projected volumes - Zarko Randelov
ic (University of Cambridge)
DTSTART;TZID=Europe/London:20200130T143000
DTEND;TZID=Europe/London:20200130T153000
UID:TALK126346AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/126346
DESCRIPTION:Given $2^n^ - 1$ real numbers $x_A$ indexed by the
non-empty subsets $A \\subset \\{ 1\,\\ldots\,n \
\}$\, is it possible to construct a body $T$ in $R
^n^$ such that $x_A = \\| T_A \\|$\, where $\\| T_
A \\|$ is the $\\| A \\|$-dimensional volume of th
e projection of $T$ onto the subspace spanned by t
he axes of $A$? As it is more convenient to take l
ogarithms\, we denote by $\\psi_n$ the set of all
vectors $x$ for which there is a body $T$\nsuch th
at $x_A = \\log \\| T_A \\|$ for all $A$. Bollob\\
'as and Thomason showed that $\\psi_n$ is containd
in the polyhedral cone defined by the class of `u
niform cover inequalities'. Tao and Zeng conjectur
ed that the convex hull of $\\psi_n$ is equal to t
he cone given by the uniform cover inequalities.\n
\nWe show that this conjecture is not right\, but
is `nearly' right.\n\nJoint work with Imre Leader
and Eero Raty.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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