Type: Seminar

Modified: Wed 21 Mar 2012 1242; Wed 21 Mar 2012 1244

Distribution: World

Expiry: 4 Apr 2012

CalTitle1: Macquarie Colloquium Lecture: Pomerance -- Sums and products

Auth: zhangou@bari.maths.usyd.edu.au

There is just a message from the organizer (earlier today, March 21) that this event has been cancelled. I am very sorry for any inconvenience this must have caused. ------------------------------------------------------ Macquarie University Mathematics Department Colloquium Lecture Room: W5C 232 Date: Wednesday, 21/03/2012 Time: 1 pm Speaker: Carl Pomerance, Dartmouth College http://www.math.dartmouth.edu/~carlp/ ------------------------------------------------------ Title: Sums and products Abstract: 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 is less than $N^{2-\e[silon}$? 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 joint work with P. Kurlberg and J. C. Lagarias. ------------------------------------------------------ We will take the speaker out to lunch at the Staff Club. The lunch party departs from level 4 of E7A at 12 noon. Please join us.