On the sum-product problem

Series: 
Other Talks
Monday, April 13, 2009 - 16:30
2 hours
Location: 
Skiles 269
,  
Math, UBC
Organizer: 
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 this talk we review some recent developments and problems related to the conjecture.