The Mahler Conjecture on Convex Bodies

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• Matthew Tointon, Cambridge
• Friday 21 October 2011, 16:00-17:00
• MR15, CMS.

If you have a question about this talk, please contact Ben Green.

Tea in Pavilion E from 3.30

If A is a centrally symmetric convex body in R^{d then we define its polar body A to be { x in R}d : < 1 for all a in A }. The Mahler volume of A is then defined to be the product vol(A)vol(A). Mahler conjectured that this volume would be minimised by cubes and octahedra; this is trivial in dimension 1 and has been resolved in dimension 2, but remains stubbornly open in dimensions 3 and higher. In searching for a general proof I came up with a proof of the 2-dimensional statement, which I shall present here. I shall then give some pointers as to why generalising this to higher dimensions is hard. If there is time at the end I hope to discuss with the audience potential approaches to the 3-dimensional problem.

This talk is part of the Discrete Analysis Seminar series.

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