Tamás Terlaky (McMaster University, Canada)

Diameter and curvature: the Hirsh Conjecture and its relatives
Joint work with Antoine Deza and Yuriy Zinchenko.
Friday 15 February 2008 at 15.30, JCMB 5326

Abstract

By analogy with the Hirsh conjecture, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities defining the polytope. By analogy with a result of Dedieu, Malajovich and Shub, we conjecture that the average diameter of a bounded cell of an arrangement is less than the dimension. We substantiate these conjectures in low dimensions, highlight additional links, and prove a continuous analogue of the d-step conjecture.

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