# 26 KAM Mathematical Colloquium

## Prof. PETER J. CAMERON

### LONDON

## SUM-FREE SETS

May 28, 1996

Lecture Room S6, Charles University, Malostranske nam. 25, Praha 1

10:30 AM

## Abstract

A set of natural numbers is {\em sum-free\/} if it does not contain the sum of two of its members. The main theme of the talk is that, from this simple condition, a very rich structure arises; and, if we use different mathematical techniques to ask the question "what does the typical sum-free set look like?", such as counting, Baire category, Hausdorff dimension, or probability, we can get very different answers. I will also discuss some occurrences of sum-free sets in Ramsey theory and in highly symmetric graphs.