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PRODID:-//Memento EPFL//
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SUMMARY:Polytopes\, linear programming\, the Hirsch conjecture\,  and open
  mathematical collaboration
DTSTART:20101118T171500
DTSTAMP:20260407T061213Z
UID:2d9d69cc858619dcb14e3d544fcecae5b0681eb497f97ffcf768f33f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Gil Kalai\nPolytopes attracted mathematicians since ancient ti
 mes. The ancient Egyptians knew quite a bit of geometry of polytopes\, and
  the pyramids are\, of course\, a special type of polytopes. The ancient G
 reek discovered the five platonic solids. Euler\, who can be regarded as t
 he father of modern graph theory proved a remarkable formula which explain
 s the relation between combinatorics and polytopes: for every polytope in 
 space with V vertices\, E edges and F faces\,\n\nV-E+F=2\n \nFor example\,
  for the cube\, V=8\, E=12\, and F=6 and indeed 8-12+6=2. \n \nPolytopes i
 n higher dimension than three were studied since the 19th century. The fir
 st rigorous proof of Euler's formula for higher dimension was obtained by 
 Poincare. Poincare used tools from algebraic topology\, a new subject of s
 tudy that he himself developed. It turns out that Euler's formula is close
 ly related to topology\, an important part of geometry. Linear programming
  which is one of the main application of mathematics also leads to excitin
 g problems about polytopes. On of these problems\, The Hirsch conjecture w
 as solved recently by Franciscos Santos after 53 years. I will describe so
 me results about polytops I will discuss also a joint collective effort "p
 olymath3" to attack a weak version of Hirsch conjecture.\n 
LOCATION:CM 1 4 https://plan.epfl.ch/?room==CM%201%204
STATUS:CONFIRMED
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