Polytopes and arrangements: diameter and curvature
- Date: 10/26/2007
Tamás Terlaky (McMaster University)
University of Calgary
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.
Joint work with Antoine Deza and Yuriy Zinchenko.
PIMS Distinguished Lecture 2007