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DESCRIPTION: It is well known that a line can intersect at most 2 n −1 cell
 s of the  n × n  chessboard. What happens in higher dimensions: how many ce
 lls of the  d -dimensional [0\, n ]^  d   box can a hyperplane intersect? W
 e answer this question asymptotically. We also prove the integer analogue o
 f the following fact. If  K\,L  are convex bodies in   R ^d  and  K  ⊂  L \
 , then the surface area  K  is smaller than that of  L . This is joint work
  with Péter Frankl. 
DTSTAMP:20220527T141700
DTSTART:20220530T160000
CLASS:PUBLIC
LOCATION:Chemistry building\n Arnimallee 22\n 14195 Berlin \n Hörsaal A
SEQUENCE:0
SUMMARY:Imre Bárány (Rényi Institute\, Budapest): Cells in the box and a hy
 perplane
UID:107920421@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20220530-C-Bar
 any.html
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