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DESCRIPTION: In 1988\, Mathieu Meyer presented a lower bound on the volum
e of a convex body in terms of the volumes of its sections with the coordin
ate hyperplanes. Our aim is to "discretize" this inequality by replac
ing the volume by the lattice point enumerator. It turns out that such a di
screte analog cannot exist for general convex bodies. Moreover\, it will no
t imply its continuous counterpart. We prove inequalities for the cas
e of o-symmetric bodies (using arithmetic progressions) and unconditional b
odies (by proving a universal bound for the lattice point enumerator of unc
onditional lattice polytopes). Moreover\, the talk will touch on a reverse
inequality and other related problems.
DTSTAMP:20191025T171700
DTSTART:20191118T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Ansgar Freyer (Technische Universität Berlin): Discrete analogs of
an inequality by Meyer
UID:95692574@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20191118-C-Freyer.html
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