Title: Sums and products


What could be simpler than to study sums and products of integers? Well
maybe it is not so simple since there is a major unsolved problem: For
arbitrarily large numbers N, can there be sets of N positive integers
where both the number of pairwise sums and pairwise products are less
than N^{2-epsilon}? Erdos and Szemeredi conjecture no. This talk is
directed at another problem concerning sums and products, namely how
dense can a set of positive integers be if it contains none of its
pairwise sums and products? For example, take the numbers that are 2 or
3 mod 5, a set with density 2/5. Can you do better? This talk reports on
recent joint work with P. Kurlberg and J. C. Lagarias.