On the Maximum Number of Rich Lines in General Position

Combinatorics Seminar
Friday, January 27, 2012 - 15:05
1 hour (actually 50 minutes)
Skiles 005
School of Mathematics, Georgia Tech
A famous theorem of Szemeredi and Trotter established a bound on the maximum number of lines going through k points in the plane. J. Solymosi conjectured that if one requires the lines to be in general position -- no two parallel, no three meet at a point -- then one can get a much tighter bound. Using methods of G. Elekes, we establish Solymosi's conjecture on the maximum size of a set of rich lines in general position.