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SUMMARY:The Mahler Conjecture on Convex Bodies - Matthew Tointon\, Cambrid
 ge
DTSTART:20111021T150000Z
DTEND:20111021T160000Z
UID:TALK33378@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:If A is a centrally symmetric convex body in R^d then we defin
 e its\npolar body A* to be { x in R^d : <x\,a> <  1  for all a in A }. The
 \nMahler volume of A is then defined to be the product vol(A)vol(A*).\nMah
 ler conjectured that this volume would be minimised by cubes and\noctahedr
 a\; this is trivial in dimension 1 and has been resolved in\ndimension 2\,
  but remains stubbornly open in dimensions 3 and higher. In\nsearching for
  a general proof I came up with a proof of the\n2-dimensional statement\, 
 which I shall present here. I shall then give\nsome pointers as to why gen
 eralising this to higher dimensions is hard.\nIf there is time at the end 
 I hope to discuss with the audience\npotential approaches to the 3-dimensi
 onal problem.
LOCATION:MR15\, CMS
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