## Sum-Product problems over various fields

#### Jozsef SolymosiUniversity of British ColumbiaMathematics

An old conjecture of Erdos and Szemeredi states that if A is a finite set of integers then the sum-set or the product-set should be large. The sum-set of A is A + A={a+b | a,b \in A}, and the product set is defined in a similar way, A*A={ab | a,b \in A}. Erdos and Szemeredi conjectured that the sum-set or the product set is almost quadratic in |A|, i.e. max (|A+A|,|A*A|)> c|A|^{2-\epsilon}. In the first lecture we review some recent developments and problems related to the conjecture.

Back to Combinatorics Tutorials