# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, November 24, 2009, 12:15 pm

**Duration**: This information is not available in the database

**Location**: CAB G51

**Speaker**: Andrea Francke

## A simple proof of the upper bound theorem (student talk, 45 min.)

The Upper Bound Theorem, first proved by McMullen in the 1970's, is one of
the most fundamental theorems about convex polytopes. The theorem gives exact
upper bounds for the maximum number of faces of a d-dimensional convex
polytope with n vertices.
In this article, a new, simple proof is given that reduces the theorem to
a purely combinatorial problem about systems of sets with certain
intersection properties, and then uses methods from (multi)linear algebra
to solve the latter.
This paper is one of the clearest and most elegant applications of linear
algebra methods in combinatorics.

Paper by Noga Alon and Gil Kalai: A simple proof of the upper bound
theorem, European Journal of Combinatorics 6 (1985), 211-214.

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