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SUMMARY:The width of 5-dimensional prismatoids - Matschke\, B (Technische 
 Universitt Berlin)
DTSTART:20130719T130000Z
DTEND:20130719T133000Z
UID:TALK46301@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Santos' construction of counter-examples to the Hirsch Conject
 ure (2012) is based on the existence of prismatoids of dimension d of widt
 h greater than d. Santos\, Stephen and Thomas (2012) have shown that this 
 cannot occur in dimension less than 5. Motivated by this we here study the
  width of 5-dimensional prismatoids\, obtaining the following results:\n\n
 - There are 5-prismatoids of width six with only 25 vertices\, versus the 
 48 vertices in Santos' original construction. This leads to non-Hirsch pol
 ytopes of dimension 20\, rather than the original dimension 43.\n\n- There
  are 5-prismatoids with n vertices and width Omega( qrt{n}) for arbitraril
 y large n. Hence\, the width of 5-prismatoids is unbounded. \n\nThis is jo
 int work with Francisco Santos and Christophe Weibel.\n
LOCATION:Seminar Room 1\, Newton Institute
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