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SUMMARY:Inequalities on projected volumes - Zarko Randelovic (University o
 f Cambridge)
DTSTART:20200130T143000Z
DTEND:20200130T153000Z
UID:TALK126346@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Given $2^n^ - 1$ real numbers $x_A$ indexed by the non-empty s
 ubsets $A \\subset \\{ 1\,\\ldots\,n \\}$\, 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 the projection of $T$ onto the subsp
 ace spanned by the axes of $A$? As it is more convenient to take logarithm
 s\, we denote by $\\psi_n$ the set of all vectors $x$ for which there is a
  body $T$\nsuch that $x_A = \\log \\| T_A \\|$ for all $A$. Bollob\\'as an
 d Thomason showed that $\\psi_n$ is containd in the polyhedral cone define
 d by the class of `uniform cover inequalities'. Tao and Zeng conjectured t
 hat the convex hull of $\\psi_n$ is equal to the 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
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