(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.

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