Leírás
Abstract:
I will talk about an old problem of Erdos: What is the maximum number
of points on the plane, no three on a line and no four on a circle,
such that any pairwise distances are integers? It is unknown if this
number exists, but the largest known construction consists of seven
points only. There are many related questions to consider. Most
notably, there is the Erdos-Ulam conjecture: there is no everywhere
dense point set on the plane such that any pairwise distances are
rational. There are two major conjectures in number theory, the
Uniformity Conjecture and the ABC Conjecture and either of them would
imply the conjecture. There are only partial results known
unconditionally.
For Zoom access please contact András Biró (biro.andras[a]renyi.hu).