(MC-DAG-7)
 

5-day minicourse on

I. Combinatorics of Convex Polytopes and the Simplex Algorithm

II. The Cube

by

Prof. Gil Kalai, Hebrew University, Israel

 

Gil Kalai was born in 1955 in Tel Aviv. He obtained his PhD in 1983 at the Hebrew University, Jerusalem, Israel. He visited M.I.T. as a postdoc in 1983-1985. He has held positions at the Hebrew University since 1985, where he is full professor since 1993. Prof.dr. G. Kalai was awarded the following prizes: S.I.A.M. Polya prize in 1992, the I.M.U. Erdos Prize in 1993 and the AMS & Math. Programming Soc. Fulkerson Prize in 1994. He was Milliman Lecturer at the University of Washington in 1994 and is Editor-in-Chief of the Israel Journal of Mathematics. He has held visiting positions at IBM, San Jose, in 1990/1991 and the Institute for Advanced Study, Princeton, Fall 1995.
 

Contents

Part 1: Combinatorics of convex polytopes and the simplex algorithm.
First basic properties of convex polytopes, their face lattices, face numbers, and flag numbers will be described. Some fundamental properties of simple polytopes will be proved and the lower bound theorem and upper bound theorem will be discussed. Some results concerning the diameter of graphs of polytopes and pivot rules for the simplex algorithm will be proved. These topics will be studied in the context of more general combinatorial objects. These objects will be discussed and we will try to present the question "Does Geometry Help?" (taken from a recent paper by Gartner). Many open problems will be presented.

Part 2: The Cube
Some recent results will be presented (mainly isoperimetric results) concerning the graph of the discrete cube and some applications will be mentioned.
 

Time and place
Eindhoven University of Technology, the Netherlands, March 13-17, 2000.
 

Admission fee
All courses are free for students and members of research groups affiliated with EIDMA. For other participants, an amount of NLG 1,500.- is due. Reductions may apply to students and members of other scientific institutes.
 

Registration
You can register by sending an e-mail to ms. Henny Houben at  eidma@win.tue.nl  before February 28, 2000.