Abstract: Noga Alon recently proved that the minimum possible size of
an epsilon-net for point objects and line ranges in the plane is
(slightly) bigger than linear in 1/epsilon. This settles a problem 
raised by Matousek, Seidel and Welzl in 1990.
His proof uses a result from Ramsey theory, known as the density 
Hales-Jewett theorem, proved by Furstenberg and Katznelson (1991).
We will give an introduction to epsilon-nets, and then talk about 
the Ramsey theory result and how it is applied to prove the lower bound.