Colloquium
3:00 p.m., Friday (October 13, 2006)
MATX 1100
Jozsef Solymosi
UBC
On the SumProduct Conjecture
Let A be a finite subset of real numbers. If A is an arithmetic progression, then A+A=2A1, and A*A > A^{2\epsilon}, where A+A={a+a': a,a' \in A} is the sumset of A and A*A={aa':a,a'\in A} is the productset. (S denotes the cardinality of S.)
Similarly, if B is an arithmetic progression and A={2^n: n \in B}, then the productset is small, A*A=2A1, but the sumset is large, A+A > cA^2.
Erdos and Szemeredi conjectured that the sumset or the productset should be always large, max (A+A,A*A) > cA^{2\delta}. (\delta goes to 0 as A goes to infinity.) In this talk we will summarize the recent results and further research directions.
Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115).
