skip to content

Positive projections

Tuesday 5th July 2011 - 14:00 to 15:00
INI Seminar Room 1
If A is a set of n positive integers, how small can the set { (a,b) : a,b in A } be? Here as usual (a,b) denotes the HCF of a and b. This elegant question was raised by Granville and Roesler, who also reformulated it in the following way: given a set A of n points in the integer grid Z^d, how small can (A-A)^+, the projection of the difference set of A onto the positive orthant, be? Freiman and Lev gave an example to show that (in any dimension) the size can be as small as n^{2/3} (up to a constant factor). Granville and Roesler proved that in two dimensions this bound is correct, i.e. that the size is always at least n^{2/3}, and they asked if this holds in any dimension. After some background material, the talk will focus on recent developments, including a negative answer to the n^{2/3} question. (joint work with Bela Bollobas)
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons