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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The width of 5-dimensional prismatoids

## The width of 5-dimensional prismatoidsAdd to your list(s) Download to your calendar using vCal - Matschke, B (Technische Universitt Berlin)
- Friday 19 July 2013, 14:00-14:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Polynomial Optimisation Santos’ construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width 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: - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos’ original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43. - There are 5-prismatoids with n vertices and width Omega( qrt{n}) for arbitrarily large n. Hence, the width of 5-prismatoids is unbounded. This is joint work with Francisco Santos and Christophe Weibel. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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