Seminar Details

How many convex quadrilaterals must occur among n points in the plane, no three of which are collinear? We will consider this question in a few small cases, and see how lower bounds in small cases induce lower bounds in general. But in order to beat the bounds that arise in this way, we must use more strongly the geometry of the underlying point set. We will demonstrate some recent techniques in this area. In the talk we will see how this question of counting convex quadrilaterals bears on the general combinatorial geometry of planar point sets.