Some recent results on combinatorial number theory

Let A\subset \Bbb C be a set of n numbers. The sum set of A is

2A=\{a_1 + a_2 \;| \; a_i \in A \},

and the product set of A is

A^2=\{a_1 a_2 \;| \; a_i \in A \}.

In a 1983 paper Erdos and Szemeredi conjectured that the sum set and the product set cannot be both small. More precisely, either the sum set or the product set should have nearly n^2 elements.

This problem is still unsolved, despite a certain amount of recent results. We will describe the present status of it and related questions of combinatorial number theory.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).