Polytopes and Arrangements : Diameter and CurvatureAlgebra & Discrete Mathematics
|Speaker:||Yuriy Zinchenko, University of Calgary|
|Start time:||Tue, May 29 2012, 2:10PM|
We introduce a continuous analogue of the Hirsch conjecture and a discrete analogue of the result of Dedieu, Malajovich and Shub. We prove a continuous analogue of the result of Holt and Klee, namely, we construct a family of polytopes which attain the conjectured order of the largest total curvature, and a continuous analogue of a d-step equivalence result for the diameter of a polytope. Potential extensions of this work will be highlighted.