The width of 5-dimensional prismatoids

Add 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
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.