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DESCRIPTION: We prove inequalities on the number of lattice points inside a
convex body K in terms of its volume and its successive minima. The succes
sive minima of a convex body have been introduced by Minkowski and since th
en\, they play a major role in the geometry of numbers. A key step in the
proof is a technique from convex geometry known as Blascke's shaking proce
dure by which the problem can be reduced to anti-blocking bodies\, i.e.\, c
onvex bodies that are "located in the corner of the positive orthant". As
a corollary of our result\, we will obtain an upper bound on the number of
lattice points in K in terms of the successive minima\, which is equivalen
t to Minkowski's Second Theorem\, giving a partial answer to a conjecture b
y Betke et al. from 1993. This is a joint work with Eduardo Lucas MarÃn.
DTSTAMP:20210629T162300
DTSTART:20210705T160000
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Ansgar Freyer (Technische UniversitÃ¤t Berlin): Shaking a convex bod
y in order to count its lattice points
UID:107919164@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210705-C-Freyer.html
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